Question

The sum of two natural numbers is 15 and the difference between their squares is 15. The difference between the numbers is ___.

Answer 1

The difference between the squares of two natural numbers is only equal to the numbers sum, if the numbers are consecutive.

Since in this case:
difference between the squares of the two numbers = 15 = the sum of the two numbers.

So the numbers must be consecutive natural numbers, that means the difference between the two numbers is 1.