Hi I'm having trouble with this step of the derivation of the chemical potential for an ideal fermi gas in the low temperature limit

I've got as far as to find

$\displaystyle $

E_F = \mu \left(1+\frac{\pi^2}{12} \left(\frac{kT}{\mu}\right)^2 + ...\right)

$

and need to invert this expression to get the chemical potential as a function of fermi energy

I've tried writing this as (which is ok as this is the same as above to first order)

$\displaystyle $

E_F = \frac{\mu}{1-\frac{\pi^2}{12} \left(\frac{kT}{\mu}\right)^2}

$

but I cant seem to get it into a form which is easily invertable any chance of a hand here please?

NB the answer I'm trying to get to is

$\displaystyle $

\mu = E_F \left(1-\frac{\pi^2}{12} \left(\frac{kT}{E_F}\right)^2 + ...\right)

$