In the present paper the authors introduce the E-2,E-1-transform with kernel the exponential integral function. It is shown that the third iterate of the L-2-transform is the exponential integral transform, and some identities involving the new transform, the L-2-transform and the Widder potential transform are given. Using the identities, Parseval-Goldstein type results involving these transforms are proved. Some illustrative examples are also given. (C) 2006 Elsevier Inc. All rights reserved.