EXHIBIT (b)

Certification of CEO and CFO Pursuant to

18 U.S.C. Section 1350,

as Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Report on Form N-CSR of Guggenheim Enhanced Equity Income Fund (the “Company”) for the period ended June 30, 2010 (the “Report”), J. Thomas Futrell, as Chief Executive Officer of the Company, and Steven M. Hill, as Chief Financial Officer, Chief Accounting Officer and Treasurer of the Company, each hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of his knowledge:

(1)   the Report fully complies with the requirements of Section 13 (a) or 15 (d) of the Securities Exchange Act of 1934; and

(2)   the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: September 2, 2010

/s/ J. Thomas Futrell

Name:  J. Thomas Futrell

Title:   Chief Executive Officer

/s/ Steven M. Hill

Name: Steven M. Hill

Title:   Chief Financial Officer, Chief Accounting Officer and Treasurer