Call the clearly vertical leg (that obviously is intended to meet the side of length 10 at a right angle) c.
Then we know that
and
Then
But
and we know that . Thus
Thus we have the system of equations
This has a solution of
and
(Which are at least close to Isomorphism's a = 8 and b = 6.)
-Dan
EDIT: Just saw your post ty2391. Obviously I agree with your answer. Good job.