The sum of two numbers is 27 and product is 182. The numbers are:

Explanation: Let x is one number
Another number = 27 – x
Product of two numbers = 182
x(27 – x) = 182
⇒ x² – 27x – 182 = 0
⇒ x² – 13x – 14x + 182 = 0
⇒ x(x – 13) -14(x – 13) = 0
⇒ (x – 13)(x -14) = 0
⇒ x = 13 or x = 14