List all two digit numbers that if reversed and added to the original number create a perfect square.
Let the digits be a and b.
Then (10a+b) + (10b+a) = 11(a+b) must be a perfect square.
This is the case if and only if a + b = 11.
So the solution is 29, 38, 47, 56, 65, 74, 83 and 92.