Dr. Casey's Alphanumeric Conundrum

In this mathematical brain-teaser a simple addition problem has been coded - that is, the digits have been replaced with letters. YOU need to figure out what letters represent what digits. Armed with your algebraic wits and powers of deduction you eliminate letter-digit pairs until only valid combinations remain and the puzzle is solved. An on-screen grid helps you narrow down the possibilities as you track down the true values of the letters. In some cases you may even find yourself using simultaneous equations to solve it! Think of it as aerobics for the cerebrum.