How does x squared minus y squared equal 901?

It can. You can make it happen. The problem is that you may not be able to get whole number answers

Here's the general equation.
x^2 - y^2 = 901 Suppose you make y =  15. what will x be?
x^2 - 15^2 = 901  
x^2 - 225 = 901        Add 225 to both sides.
x^2 = 1126               Now take the square root of 1125
sqrt(x^2) = sqrt(1126)
x = +/- 33.556 
That's one example. Just pick others and use your square root button. I don't think there's a whole number answer, but I could be wrong.