Read between the lines
Discern a meaning which isn't made obvious or explicit.
This expression derives from a simple form of cryptography, in which a hidden meaning was conveyed by secreting it between lines of text. It originated in the mid 19th century and soon became used to refer to the deciphering of any coded or unclear form of communication, whether written or not; for example, one might say "She said she was happy to go to the party but didn't seem concerned when it was cancelled. Reading between the lines, I don't think she wanted to go in the first place".
The first example that I can find of the phrase in print is from The New York Times, August 1862:
Earl Russell's dispatch does not recite the terms of the note to which it is a reply, the letter assumes a somewhat enigmatical character, and the only resource we have is, as best we may, to "read between the lines" of this puzzling, but important, communication of the British Foreign Secretary.