Reciprocal Solution to the Ramberg Osgood Equation

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The Ramberg Osgood equation relates the stress in an elastic plastic material to the strain.

$\epsilon_a=\frac{\sigma_a}{E}+(\frac{\sigma_a}{A})^\frac{1}{n}$

$E$ and $A$ are both bigger than $\sigma_a$

As for $n$ it should be smaller than 1.

The reason I want to solve this equation's reciprocal is because we sometimes obtain $\epsilon_a$ and we need to solve for $\sigma_a$

Any help would be appreciated, because I can't seem to find a way to solve it with my current math tools.

Note: I know this can be solved numerically with countless ways, but I was searching for a closed formula