Let the numbers be ‘a’ and ‘b’.

Given, sum of two numbers is 48 and their product is 432.

⇒ a + b = 48

⇒ a = 48 – b

Also, ab = 432

⇒ 48b – b² = 432

⇒ b² – 48b + 432 = 0

⇒ b² – 36b – 12b + 432 = 0

⇒ b(b – 36) – 12(b – 36) = 0

⇒ (b – 12)(b – 36) = 0

⇒ b = 12, 36