The product of two numbers is 36 and their sum is 37. what is their difference?

Hello,
Let's be a the greatest number, b the smallest

Method 1:

a+b=37 ==>b=37-a
a*b=36==>a(37-a)=36
==> a²-37a+36=0
==>a²-36a-a+36=0
==>a(a-36)-(a-36)=0
==>(a-36)(a-1)=0
(a=36 and b=37-36=1) or (a=1 and b=37-1=36) but a>b ==>exclude
==>a-b=35

Method 2:

a*b=36
a+b=37 ==>(a+b)²=37²
(a+b)²-4ab=37²-4*36
==>a²+2ab+b²-4ab=1225
==>(a-b)²=35²
==>a-b=35 or a-b=-35 (to exclude since a>b)