One number is 5 more than another. the difference between their squares is 155. what are the numbers

the smaller number is 13 and the larger one is 18.

Let's say that the smaller number is x and the larger one is y.

Giving the equation x + 5 = y

This would also make the equation y^2-x^2 = 155

to solve let's simplify to find what y^2 is in x terms.

y^2 = (x+5) (x+5) = x^2 + 10x + 25.

therefore x^2 + 10x + 25 - x^2 = 155

10x + 25 = 155

10x = 130

x = 13

y = 18