Find two numbers based on their sum/difference

Two logicians must find two distinct integers AA and BB such that they are both between 2 and 100 inclusive, and AA divides BB. The first logician knows the sum A+B A + B and the second logician knows the difference BAB-A.

Then the following discussion takes place:

Logician 1: I don't know them.
Logician 2: I already knew that.

Logician 1: I already know that you are supposed to know that.
Logician 2: I think that... I know... that you were about to say that!

Logician 1: I still can't figure out what the two numbers are.
Logician 2: Oops! My bad... my previous conclusion was unwarranted. I didn't know that yet!

What are the two numbers?

Enter your answer as a decimal number A.BA.B.
((For example, if A=23A=23 and B=92B=92, write 23.92.)23.92.)

Note: In this problem, the participants are not in a contest on who finds numbers first. If one of them has sufficient information to determine the numbers, he may keep this quiet. Therefore nothing may be inferred from silence. The only information to be used are the explicit declarations in the dialogue.


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