Q:

Equation with tangent and powers

I need to solve this equation for x:
$$2000 \sigma = 1 - \frac{20x}{\pi^2x^2 + 100} - \frac{2 \arctan(\frac{\pi x}{10})}{\pi} $$
$\sigma$ is a known value. I need to solve this for $ \sigma = 10^{-5}$, $\sigma = 10^{-10}$  and  $\sigma = 10^{-15}$
As $x$ is inside the $\arctan$ and squared I cannot get a solution. 
Can anybody help me?
Thank you!

A:

i have found with Maple
$\sigma=10^{-5}$ and $x\approx 8,34475638$
$\sigma=10^{-10}$ and $x \approx 409,0338318$
$\sigma=10^{-15}$ and $x \approx 18986,12832$

