x = one positive number
y = other positive number
x  y = 27 ← difference is 27
xy = 2680 ← product is 2680
x  y = 27 ← first equation
x = y + 27 ← added y to each side
xy = 2680 ← second equation
(y + 27)y = 2680 ← substituted (y + 27) for x
y² + 27y = 2680 ← distributive property
y² + 27y  2680 = 0 ← subtracted 2680
(y + 67)(y  40) = 0 ← factored
y + 67 = 0 or y  40 = 0 ← set equal to zero
y = 67 or y = 40 ← solved
40 and 67 are the two numbers
 Proof
