In the S06E09 of Game of Thrones, "Battle of the Bastards", Tyrion argues with Daenerys that burning cities to the ground is not a good choice in war. He reveals to her the real reason Jaime, the Kingsguard, killed his King, the Mad King.
I am pretty sure that Brienne is the only person to whom Jaime reveals this truth, both in the books and in the show onscreen. I don't think Jaime ever revealed it to Tyrion on-screen in the show (I might be wrong, please point to the scene if I am). Do the books have a conversation between them regarding this, or is it also implied off-paper (for a lack of a better term).