Let a number be x.

Then the other number = 27 - x

Product of the numbers = x(27 - x) = 27x - x²

By problem 27x - x² = 182

x² - 27x + 182 = 0

x²-x - 13x + 182 = 0

x(x - ) - 13(x - ) = 0

(x - 13)(x - ) = 0

x - 13 = 0 or x - = 0

x = 13 or

∴The numbers are 13; 27 - 13 = 14 or 14 and 27 - = .