There is also another formula which is confusing

Make e the subject

T = (1 + e/1 – e) x √L/10

T = \frac{1+e}{1-e}\ \times \ \frac{\sqrt{L}}{10}

Is that it?

Sorry, I mistyped it there is meant to be a 5 instead of a 10, and the square root is over the whole of L/5

Ok, so;

T = \frac{1+e}{1-e} \times \sqrt{\frac{L}{5}}

Multiply by 1-e, on both sides:

T(1-e) = \frac{1+e}{\cancel{1-e}} \times \sqrt{\frac{L}{5}} \times \cancel{(1-e)}

Expand both sides:

T-eT = \sqrt{\frac{L}{5}} +e\sqrt{\frac{L}{5}}

Bring all the 'e' on one side:

T\cancel{-eT + eT} - \sqrt{\frac{L}{5}} = \cancel{\sqrt{\frac{L}{5}}} +e\sqrt{\frac{L}{5}}+ eT\cancel{ - \sqrt{\frac{L}{5}}}

T- \sqrt{\frac{L}{5}} = e\sqrt{\frac{L}{5}}+ eT

Then factorise e;

T - \sqrt{\frac{L}{5}} =e(\sqrt{\frac{L}{5}}+ T)

It's nearly finished, can you take it now? :)

I hope it helped! :)