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

Let the first number be x, then the second number will be 27-x.
x(27-x) = 182
=> 27x - x² = 182
=> x² - 27x + 182 = 0
=> x² - 13x - 14x + 182 = 0
=> x(x - 13) - 14(x - 13) = 0
=> (x - 14)(x - 13) = 0
=> x = 14, 13
If the first number is 14, then the second number is 13 and if the first number is 13, then the second number is 14.