E must be 2, since even 100^3 is greater than six digits long.
So there are only five letters remaining that could take the values of 3, 4, 6, 7, and 8, and the only English word you can make from them is BRAVO.
Just to confirm, we can substitute back into the original problem, which gives us 874^2 = 763876, so this is indeed the solution.
Posted by tomarken
on 2014-06-13 10:21:51