I think the first sentence means that you have two numbers, say x and y, and they are each squared... this gives you x^2 and y^2 (two "new numbers").
Then x^2 - y^2 < 10
x - y = 1
x + y > 7
Multiply the last two together to get
x^2 - y^2 = (x + y)(x - y) > 7 * 1 = 7