Last Saturday, I drove to Rockville, MD to visit my parents. As usual, I stopped by the huge Kamkin bookstore of Russian literature. For $4, I bought there a Russian translation of Jeux et casse-tête a programmer by Jacques Arsac, Dunod, 1985.

Problem 15, Ch. 1 is exactly your problem with insignificant variations. In a free translation, the conversion appears as:

P: I can't find the two numbers.
S: I know you can't.
P: If so, I can.
S: Then I also can.

No solution is given, except for suggestions how to write a program that sieves out unwanted numbers. The claim is that, as the result, only one pair of numbers remains. It's then bound to be 4, 13.