Now I'm stabbing in the dark.... Multiply both sides by $\displaystyle t^2$:

$\displaystyle \frac{d^2}{c^2} = t^2 [1 - (\frac{mc^2}{e + mc^2})^2]$

This is getting hairy. Isolate $\displaystyle t^2$ on the RHS:

$\displaystyle \frac{d^2}{c^2[1 - (\frac{mc^2}{e + mc^2})^2]} = t^2$

Swap sides (easy):

$\displaystyle t^2 = \frac{d^2}{c^2[1 - (\frac{mc^2}{e + mc^2})^2]}$

Take square root of both sides:

$\displaystyle t = \sqrt{\frac{d^2}{c^2[1 - (\frac{mc^2}{e + mc^2})^2]}}$

Now try to simplify this MATHEMATICAL MONSTROSITY.

Continued next post....