Let x = the first positive integer

y = the second positive integer

Equations:

xy=240

x - y = 8

Solution (use the substitution method in solving two equations in two variables):

x - y = 8

x = y+8

xy = 240

(y+8)y=240

y2 + 8y = 240

y2 + 8y - 240 = 0

(y-12)(y+20)=0

y - 12 = 0 and y + 20 = 0

y = 12 and y = -20

But since we're looking for positive integers only, the answer is 12 only. Substitute this to the other equation.

y = 12

xy = 240

x(12)=240

12x=240

x = 240/12

x = 20

The two positive integers are 12 and 20.