Let's call those two numbers x and y. We will "translate" the information given to us into equations.
"the difference of 2 numbers is 90" -----> x - y = 90
"and their quotient is 10" -------> x/y = 10
Now you have a system of two equations:
x - y = 90
x/y = 10
You can solve it a few ways. Let's use substitution. We will rewrite the 2nd equation as x in terms of y, then substitute x in the 1st equation:
Rewriting the 2nd equation gives us: x = 10*y
Now in the first equation, replace x by 10*y. That is substitution -----> 10y - y = 90 ----> 9y = 90 ----> y = 10
See how substitution gets you an equation where you can easily solve one variable?
Now that know y = 10, you can plug 10 into any of the 2 equations of your system. If you choose the 1st equation:
x - 10 = 90
I will let you solve this simple equation.