**Let the numbers be ‘a’ and ‘b’. **

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

⇒ a^{2} – b^{2} = 180

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

⇒ b^{2 }= 8a

Thus, a^{2} – 8a – 180 = 0

⇒ a^{2} – 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 = b**^{2 }

⇒ b = 12

**Numbers are 12, 18 or -12, 18**