The sum of two numbers 10 and the difference of those two numbers is 18 (use f to represent the first number and s to represent the second number)

F + s = 10

| f - s | = 18



This means that:

f = 10 - s

And also that:

| f - s | = 18

(f-s)²=18²

f²- 2sf + s² = 324

But f=10-s

So...

(10-s)² - 2s(10-s) + s² = 324

(10-s)(10-s) - 20s + 2s² + s² = 324

100 - 20s + s² - 20s + 2s² + s² = 324

4s² - 40s + 100 = 324

4s² - 40s + 100 - 324 = 0

4s² - 40s - 224 = 0

1/4 * (4s² - 40s - 224) = 1/4 * 0

s² - 10s - 56 = 0

(s-14)(s+4)=0

So s can be either 14 or -4.

When s = 14, f = -4.

When s = -4, f = 14.