Exhibit (a)(1)(E)

LETTER TO BROKERS, DEALERS, ETC.

CASH OFFER

For All Ordinary Shares

(Including Ordinary Shares Represented by American Depositary Shares)
of

ELAN CORPORATION, PLC

by

ECHO PHARMA ACQUISITION LIMITED

THE OFFER AND RELATED WITHDRAWAL RIGHTS WILL EXPIRE AT 8:00 A.M. (NEW YORK CITY TIME) / 1:00 P.M. (IRISH TIME) ON MAY 31, 2013, UNLESS THE INITIAL OFFER PERIOD IS EXTENDED. ELAN ADSs TENDERED PURSUANT TO THE OFFER MAY BE WITHDRAWN AT ANY TIME PRIOR TO THE EXPIRATION OF THE INITIAL OFFER PERIOD AS IT MAY BE EXTENDED. ELAN ADSs MAY NOT BE WITHDRAWN DURING THE SUBSEQUENT OFFER PERIOD, EXCEPT IN THE LIMITED CIRCUMSTANCES DESCRIBED IN THE OFFER DOCUMENT.

May 2, 2013

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

Echo Pharma Acquisition Limited, a private limited company incorporated under the laws of Ireland (“Royalty Pharma”), is offering to purchase all of the issued and to be issued ordinary shares, of €0.05 each (“Elan Shares”), of Elan Corporation, plc, a public limited company incorporated under the laws of Ireland (“Elan”), including those Elan Shares represented by American depositary shares (“Elan ADSs”), subject to the terms and conditions set forth in the Cash Offer, dated May 2, 2013 (the “Offer Document”), the ADS Letter of Transmittal (as defined below) and the other relevant offer documents (the offer reflected by such terms and conditions, together with any amendments or supplements thereto, constitutes the “Offer”). Certain terms used and not otherwise defined herein shall have the respective meanings assigned to them in the Offer Document.

As discussed in the Offer Document, the Offer is not being made in any jurisdiction in which the Offer would be unlawful under the laws of such jurisdiction. No copies of the Offer Document, the ADS Letter of Transmittal or any other related documentation should be sent to any jurisdiction where to do so would constitute a violation of the relevant laws in such jurisdiction.

YOUR PROMPT ACTION IS REQUESTED. WE URGE YOU TO CONTACT YOUR CLIENTS AS PROMPTLY AS POSSIBLE. PLEASE NOTE THAT THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 8:00 A.M. (NEW YORK CITY TIME) / 1:00 P.M. (IRISH TIME) ON MAY 31, 2013, UNLESS THE INITIAL OFFER PERIOD IS EXTENDED.

For your information and for forwarding to those of your clients for whom you hold Elan ADSs registered in your name or in the name of your nominee, we are enclosing the following documents:

1. The Offer Document;

2. The ADS Letter of Transmittal to be used by holders of Elan ADSs to accept the Offer; and

3. A printed form of letter that may be sent to your clients for whose account you hold Elan ADSs registered in your name or in the name of a nominee, with space provided for obtaining such clients’ instructions with regard to the Offer.

Please note the following:

1. There are three alternatives as to the offer price based on whether the Elan Balance Sheet Confirmation Requirement is satisfied and whether the Elan Net Cash exceeds the Elan Net Cash Threshold. The three alternatives are:

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Alternative 1: If Elan does not satisfy the Elan Balance Sheet Confirmation Requirement by 12:00 noon (New York City time) / 5:00 p.m. (Irish time) on June 17, 2013 (the Relevant Date), then: (a) the cash component of the consideration will be $10.25 per Elan Share (including each Elan Share represented by an Elan ADS); and (b) Elan Stockholders who accept the Offer will also receive Net Cash Rights entitling them to receive a potential further payment of up to $1.00 per Elan Share (including each Elan Share represented by an Elan ADS) no later than 60 days following the Unconditional Date, dependent on the actual amount of Elan Net Cash. Further details of the Net Cash Rights are set out in paragraph 6 (Net Cash Rights) of the letter from the Chairman of Royalty Pharma to Elan Stockholders contained in the Offer Document and in paragraph 8 (Net Cash Rights) of Appendix III of the Offer Document. In the event that the Net Cash Rights are issued, each Net Cash Right will have a minimum value of $0.00 and a maximum value of $1.00, and Royalty Pharma can provide no assurance as to its actual value. Even if the Elan Net Cash exceeds the Elan Net Cash Threshold, the maximum value of each Net Cash Right will be $1.00. As a result, if Elan has not satisfied the Elan Balance Sheet Confirmation Requirement by the date you tender your shares in acceptance of the Offer, you should not tender unless you are willing to accept an offer price of $10.25.

Alternative 2: If Elan satisfies the Elan Balance Sheet Confirmation Requirement and announces or confirms that the Elan Net Cash equals or exceeds the Elan Net Cash Threshold, then the offer price will be $11.25 in cash for each Elan Share (including each Elan Share represented by an Elan ADS) and no Net Cash Rights will be issued as they are not required.

Alternative 3: If Elan satisfies the Elan Balance Sheet Confirmation Requirement and announces or confirms that the Elan Net Cash is less than the Elan Net Cash Threshold, then, for each Elan Share (including each Elan Share represented by an Elan ADS), Elan Stockholders who accept the Offer will receive the offer price of $11.25, reduced by the Elan Balance Sheet Confirmation Adjustment, which adjustment is up to a maximum of $1.00 and which is described in detail in paragraph 5 (The Elan Balance Sheet Confirmation Requirement) of the letter from the Chairman of Royalty Pharma to Elan Stockholders contained in the Offer Document, in cash.

Not later than 5:00 p.m. (New York City time) / 10:00 p.m. (Irish time) on June 17, 2013, Royalty Pharma will confirm the offer price and whether Net Cash Rights will be issued (based on whether the Elan Balance Sheet Confirmation Requirement is satisfied and the Elan Net Cash position) by issuing an announcement. Such confirmation will also be dispatched by mail to Elan Stockholders as soon as practicable thereafter.

For the avoidance of doubt, in the event that Offer becomes or is declared unconditional in all respects prior to the satisfaction of the Elan Balance Sheet Confirmation Requirement, Elan Stockholders who accept the Offer will receive $10.25 per Elan Share (including each Elan Share represented by an Elan ADS) and Net Cash Rights entitling them to receive a further payment of up to $1.00 per Elan Share (including each Elan Share represented by an Elan ADS) no later than 60 days following the Unconditional Date, dependent on the actual amount of Elan Net Cash.

2. The Offer is being made for all of the issued and to be issued Elan Shares, including those represented by Elan ADSs.

3. The Initial Offer Period will expire at 8:00 a.m. (New York City time) / 1:00 p.m. (Irish time) on May 31, 2013, unless Royalty Pharma extends the Initial Offer Period. If the Offer becomes or is declared unconditional on or after July 1, 2013, the Initial Offer Period will end and a subsequent offer period of at least 14 days in length will start immediately. Royalty Pharma may extend the subsequent offer period beyond 14 days until a further specified date or until further notice. You may withdraw acceptances under the Offer at any time until the end of the Initial Offer Period. Acceptances may not be withdrawn during the subsequent offer period, except in certain limited circumstances described in the Offer Document.

4. If a holder of Elan ADSs tenders its Elan ADSs in the Offer, and the Offer becomes or is declared unconditional, The Bank of New York Mellon (the “ADS Tender Agent”), as such holder’s representative, will, upon the request of Royalty Pharma, surrender the tendered and

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accepted Elan ADSs to Citibank, N.A., or its successor, as Depositary for the Elan ADSs (the “ADS Depositary”), and instruct the ADS Depositary on behalf of such holder of Elan ADSs to withdraw the Elan Shares represented by such tendered Elan ADSs and to deliver such shares to or as instructed by Royalty Pharma. Royalty Pharma will withhold up to $0.05 per Elan ADS (the “Cancellation Fee”) from the consideration payable to tendering ADS holders to pay the fees of the ADS Depositary for the surrender of the Elan ADSs and delivery of the Elan Shares represented thereby if such surrender and delivery is requested by Royalty Pharma. That money will be paid to the ADS Depositary at the time the tendered and purchased ADSs are surrendered by or at the discretion of Royalty Pharma for the purposes of the withdrawal of the Elan Shares represented thereby.

5. The Offer is conditional upon, among other things: (a) Royalty Pharma receiving valid acceptances of the Offer, that have not been validly withdrawn, in respect of not less than 90% (or such lower percentage as Royalty Pharma may decide) of the maximum number of Elan Shares (including Elan Shares represented by Elan ADSs) in issue (but excluding any such Elan Shares which are cancelled after the date of the Offer Document or which are held, or become held, in treasury) or which may be issued pursuant to the exercise of outstanding subscription, conversion or other rights, which carry, or if allotted and issued, or re-issued from treasury, would carry, not less than 90% (or such lower percentage as Royalty Pharma may decide) of the voting rights attaching to such shares; provided, that this condition will not be satisfied unless Royalty Pharma has acquired or agreed to acquire Elan Shares, including those represented by Elan ADSs, in issue or unconditionally allotted pursuant to the exercise of outstanding subscription, conversion or other rights, carrying in aggregate more than 50% of the voting rights then exercisable at a general meeting of Elan, subject to certain requirements of the Irish Takeover Rules and US tender offer rules (subject to certain exemptive relief which has been granted in respect of the Offer by the Securities and Exchange Commission); and (b) there having been received all applicable competition and antitrust approvals, including any such approvals required from the European Commission, and all applicable waiting periods under applicable competition or antitrust laws, including under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended, having expired or terminated prior to the latest time the Offer may become or be declared unconditional as to acceptances in accordance with the Irish Takeover Rules. Further detail with respect to the foregoing conditions and details of the other conditions to which the Offer is subject are described in the Offer Document under the heading “Appendix I—Conditions and further terms of the Offer.”

6. Acceptances of the Offer by holders of Elan ADSs will be made only after (a) in the case of a book-entry holder, book-entry transfer of such Elan ADSs into the ADS Tender Agent’s account at the Book-Entry Transfer Facility and delivery of an Agent’s Message, or (b) in the case of Elan ADSs registered in the name of the tendering holders and not held through the Book-Entry Transfer Facility, a properly completed and duly executed letter of transmittal for use in connection with accepting the Offer in respect of such Elan ADSs (the “ADS Letter of Transmittal”), any Elan ADRs evidencing tendered Elan ADSs, and any other required documents are delivered to the ADS Tender Agent, in each case in accordance with the procedures set forth in the section of the Offer Document entitled “Procedure for acceptance of the Offer for holders of Elan ADSs.” Settlement of the consideration to which accepting Elan Stockholders are entitled under the Offer will be consistent with United States practice and will be effected (a) in the case of acceptances of the Offer received, complete in all respects, by the Unconditional Date, within 14 calendar days of such date and (b) in the case of acceptances of the Offer received, complete in all respects, after the Unconditional Date, but while the Offer remains open for acceptance, within 14 calendar days of such receipt.

7. Royalty Pharma will pay any stock transfer taxes (but not the Cancellation Fee) applicable to the transfer of Elan ADSs pursuant to the Offer, except as otherwise provided in the ADS Letter of Transmittal.

Royalty Pharma will not pay any commissions or fees to any broker, dealer or other person (other than MacKenzie Partners, Inc. (the “Information Agent”), Capita Registrars (Ireland) Limited (the “Irish Receiving Agent”) and the ADS Tender Agent, as described in the Offer Document) for

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soliciting tenders of Elan Shares, including those represented by Elan ADSs, pursuant to the Offer. You will, however, upon request, be reimbursed for customary clerical and mailing expenses incurred by you in forwarding the enclosed materials to your clients.

Any inquiries you may have with respect to the Offer should be addressed to the Information Agent at the addresses and telephone numbers set forth on the last page of the ADS Letter of Transmittal. Additional copies of the enclosed materials may be obtained from the Information Agent.

Very truly yours,

ECHO PHARMA ACQUISITION LIMITED

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL CONSTITUTE YOU OR ANY OTHER PERSON THE AGENT OF ROYALTY PHARMA, THE IRISH RECEIVING AGENT, THE ADS TENDER AGENT, OR THE INFORMATION AGENT OR AUTHORIZE YOU OR ANY OTHER PERSON TO GIVE ANY INFORMATION OR MAKE ANY REPRESENTATION ON BEHALF OF ANY OF THEM WITH RESPECT TO THE OFFER NOT CONTAINED IN THE OFFER DOCUMENT OR THE ADS LETTER OF TRANSMITTAL.

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