help

My strategy:

After analyzing the two equations, we can conclude that A and B must be perfect square integers.

As both of their square roots end up forming integers after being added by eachother.

So I would guess and check from there.

They both should be less than 121 because the largest integer in the equations is 11.

So I would guess all perfect squares from 1 to 121.

Not the best strategy...

Nothing wrong with your strategy CalculatorUser; though a graphical approach might help your guess and check part: