Find the two numbers whose sum is 27 and product is 182.

Let one number is x. Then another number is 27-x.
Then by the given condition,
x(27-x) = 182
27x- x²-182 = 0
x²-27x+182 = 0
x²-14x-13x+182 = 0
x(x-14)-13(x-14) = 0
(x-14)(x-13) = 0
x-14 = 0
x =14
or, x-13 = 0
x =13
Hence the required two numbers are 13 and 14.