Originally posted by crazyblue

........S...L...E...D...G...E
-......H...A...M...M...E...R
-------------------------------
............G...R...E...A...T

so this is a 2-in-1 puzzle:
a) solve this or show there is no solution
b) find a result-word that brings a solution

I started my solution for this by turning it into an equivalent addition problem.

HAMMER + GREAT = SLEDGE

The R + M/T = E combinations were of particular note and so I began listing workable combination of the four to examine, one by one.

For each of these, examining E+A=G and A+G=1L were enough to quickly discover a solution for the specific case.

As it happens, SLEDGE - HAMMER + GREAT has 2 answers which will fit to create a true equation, with each letter having a unique value.

I will post those solutions to crazyblue.