PROSPECTUS SUPPLEMENT
(TO PROSPECTUS DATED JUNE 5, 1998)
 
                             TRIARC COMPANIES, INC.
                  $360,000,000 PRINCIPAL AMOUNT AT MATURITY OF
          ZERO COUPON CONVERTIBLE SUBORDINATED DEBENTURES DUE 2018 AND
            SHARES OF COMMON STOCK ISSUABLE UPON CONVERSION THEREOF
 
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     This Prospectus Supplement, together with the Prospectus, is to be used by
certain holders of the above-referenced securities or by their transferees,
pledgees, donees or their successors in connection with the offer and sale of
the above-referenced securities. The last reported sale price of the Common
Stock on the New York Stock Exchange on July 30, 1998 was $22 3/16 per share.
 
     The Prospectus dated June 5, 1998 relating to the offer for resale of up to
$360,000,000 aggregate principal amount at maturity of Triarc Companies, Inc.'s
Zero Coupon Convertible Subordinated Debentures due 2018 and the shares of
Common Stock issuable upon conversion thereof is hereby supplemented to include
the following information in the table under the heading 'Selling
Securityholders' on page 52:
 
                            SELLING SECURITYHOLDERS
 


                                                                      PRINCIPAL AMOUNT                     NUMBER OF SHARES
                                                                       AT MATURITY OF      PERCENTAGE      OF COMMON STOCK
                                                                         DEBENTURES            OF         BENEFICIALLY OWNED
                                                                     BENEFICIALLY OWNED    DEBENTURES        AND OFFERED
                      SELLING SECURITYHOLDER                         AND OFFERED HEREBY    OUTSTANDING       HEREBY(1)(2)
                      ----------------------                         ------------------    -----------    ------------------
                                                                                                 
AAM/Zazove Institutional Income Fund, L.P.........................       $5,800,000             1.6             54,897
Zazove Convertible Fund, L.P. ....................................        6,450,000             1.8             61,049

 
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(1) Represents shares of Common Stock issuable upon conversion of the
    Debentures.
 
(2) Assumes a conversion rate of 9.465 shares per $1,000 principal amount at
    maturity and a cash payment in lieu of any fractional share interest, which
    conversion rate is subject to adjustment as described under 'Description of
    Debentures -- Conversion of Debentures.' Accordingly, the number of shares
    of Common Stock issuable upon conversion of the Debentures may increase or
    decrease from time to time. Under the terms of the Indenture, the Company is
    not required to issue fractional shares of Common Stock upon conversion of
    the Debentures and, in lieu thereof, will pay cash.
 
                            ------------------------

     SEE 'RISK FACTORS' BEGINNING ON PAGE 14 OF THE ACCOMPANYING PROSPECTUS FOR
A DISCUSSION OF CERTAIN FACTORS THAT SHOULD BE CONSIDERED BY PROSPECTIVE
PURCHASERS OF THE SECURITIES OFFERED HEREBY.
 
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THESE SECURITIES HAVE NOT BEEN APPROVED OR DISAPPROVED BY THE SECURITIES AND
   EXCHANGE COMMISSION OR ANY STATE SECURITIES COMMISSION NOR HAS THE
     SECURITIES AND EXCHANGE COMMISSION OR ANY STATE SECURITIES
       COMMISSION PASSED UPON THE ACCURACY OR ADEQUACY OF THIS
        PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A
                              CRIMINAL OFFENSE.
 
               THIS PROSPECTUS SUPPLEMENT IS DATED JULY 31, 1998.