let 'x' and 'y' represent the numbers, x>0, y>0

The sum of 2 positive number is 18

x + y = 18

y = 18 - x

their product is 72

x*y = 72

plug y = 18 - x into the last equations

x*(18 - x) = 72

by solving we find

x1 = 12

x2 = 6

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for x = 12 we have y = 18 - 12 = 6

for x = 6 we have y = 18 - 6 = 12

the two numbers are 6 and 12.