The sum of two numbers is 118. if four times the smallest numbers is subtracted from the largest number the result is 18. find the two numbers.

Let's say the two numbers are "a" and "b"
"a" being the smaller one, and "b" the larger one

so, their sum is 118, or a + b = 118

if 4 times the smallest, or 4*a or 4a
is subtracted from the largest, "b",  so  b - 4a
equals 18, so b - 4a = 18

thus    

solve for "a", to find the smaller one

what's b?   well, b = 118 - a