Let the numbers be ‘a’ and ‘b’.

Given, difference of the squares of two numbers is 180.

⇒ a² – b² = 180

Also, square of the smaller number is 8 times the larger.

⇒ b² = 8a

Thus, a² – 8a – 180 = 0

⇒ a² – 18a + 10a – 180 = 0

⇒ a(a – 18) + 10(a – 18) = 0

⇒ (a + 10)(a – 18) = 0

⇒ a = -10, 18

Thus, the other number is

324 – 180 = b²

⇒ b = �12

Numbers are 12, 18 or -12, 18