I'm afraid VLOOKUP would not suit in your case because the value to be looked up is to the left of the linking value. However INDEX and MATCH in combination should suit:
Assumes your two lists are in the same workbook (and on same sheet for the sake of the image).
Edit assuming different sheets and better image:
Here Sheet1 ColumnA has been given the name EClist
and Sheet1 ColumnB AccList
.
Edit In view of your preference for VLOOKUP and given that I was wrong to expect someone else to have come along by now and offered that solution (again), I suggest copying ColumnA of Sheet1 to ColumnC and in B1 of your (assumed) other sheet:
=VLOOKUP(A1,Sheet1!B:C,2,0)
copied down to suit.