Triloma EIG Energy Income Fund - Term I SC TO-I Issuer tender offer statement

Exhibit 99.A

Cover Letter to Offer to Purchase

Exhibit A

TRILOMA EIG ENERGY INCOME FUND - TERM I

Cover Letter to Offer to Purchase

If You Do Not Want to Sell Your Shares at This Time,

Please Disregard This Notice.

This Is Solely Notification of the Fund’s Tender Offer.

November 28, 2016

Dear Triloma EIG Energy Income Fund - Term I Shareholder:

We are writing to inform you of important dates relating to a tender offer by Triloma EIG Energy Income Fund - Term I (the “Fund”). If you are not interested in tendering any of your shares in the Fund (“Shares”) for purchase by the Fund at this time, please disregard this notice and take no action.

The tender offer period will begin on November 28, 2016. All tenders of Shares must be submitted or may be withdrawn no later than 5:00 p.m., Eastern Time, on December 23, 2016. The purpose of the tender offer is to provide liquidity to Shareholders of the Fund. Shares may be presented to the Fund for purchase only by tendering them during one of the Fund’s announced tender offers.

·Should you wish to tender any of your Shares for purchase by the Fund during this tender offer period please complete and return the Investor Direction Form by no later than December 23, 2016.

·If you do not wish to sell your Shares, simply disregard this notice. NO ACTION IS REQUIRED IF YOU DO NOT WISH TO SELL ALL OR ANY PORTION OF YOUR SHARES AT THIS TIME.

All tenders of Shares must be received by the Tabulation Agent, either by mail or via the online portal, in good order no later than 5:00 p.m., Eastern Time, on December 23, 2016.

If we may be of further assistance, please contact shareholder services by calling 1-844-229-7674, Monday through Friday (except holidays), from 8:00 a.m. to 5:00 p.m., Eastern time.

Sincerely,

Triloma EIG Energy Income Fund - Term I

A-1