Let the two numbers be A and B.
A + B = 27
A B = 182 = 13*7*2*1
Let us find A and B by factors method.
A and B can be possibly from the list of the following :
1, 2, 7, 13, 14, 26, 91, 182
Take the left most factor and right most factor and then check if sum is 27. Continue to the next factor from left. So check 1 & 182 ; 2 & 91 ; 7 & 26 ;
If you choose 13 and 14 as A and B, then A+B = 27 and AB = 182.
So A = 13 and B = 14