Self Referential Puzzle - medium 2
Pyth, 104 bytes
f!s[nhd-8xd3@.+d+3@d1nh@d2/d4nh@d3/d0!&amp;/3@d4!-/d0/d@d4!-10x_d1@d5n@d6a4@.+d6n@d7@d@d7!+3@d8@ds/LdS3)^U5T

It... uh... takes a while to run. Try it online... if the server doesn't time out or run out of memory.
Explanation coming SoonTM.  Prints all the valid solutions as a 0-based list (ten elements long in which A is represented by 0, B by 1, and so on).
This is a naive solution that can probably be golfed a lot.  Just wanted to get something out there.