Let the two numbers be x and y, with x > y. Then I have two equations: x + y = 6 and x^2 - y^2 = 12. I want to find x - y, which is the positive difference of the two numbers. I notice that the second equation can be factored as (x + y)(x - y) = 12. This gives me an idea: I can use the first equation to substitute for x + y in the second equation. This way, I get (6)(x - y) = 12. Dividing both sides by 6, I get x - y = 2. This is exactly what I wanted to find, so I am done. 
The sum of two numbers is 6. The difference of their squares is 12. What is the positive difference of the two numbers?