To solve this equation, we can first combine the terms by finding a common denominator.

The equation will then become:

80(18-x) + 80(18+x) = 9(18-x)(18+x)

Expanding both sides:

80(18) - 80x + 80(18) + 80x = 9(324 - x^2)

Simplifying:

1440 = 2916 - 9x^2

Rearranging:

9x^2 = 2916 - 1440
9x^2 = 1476

Dividing by 9:

x^2 = 164

Taking the square root of both sides:

x = ±√164

Therefore, x = ± 2√41

So the solutions to the equation are x = 2√41 and x = -2√41.