Complex equation to solve

Hi,

I'm a network engineer working on a quite complex research about routing protocols. I managed to model my problem and I obtained an equation that I'm unfortunately unable to solve. I'm attaching an image below (trying to use Latex code resulted in a too big image according to edit rules) and the Latex code too.

http://elbuild.it/equation.png

<LateX Code>

\displaystyle\Biggl[\displaystyle\biggl[\frac{[1-k^{i+1}]^2-[1-k^{i}]^2}{[1-k^{N+1}]^2}\biggr] \cdot \displaystyle\biggl[\frac{P_0\tau}{1-k^{P_L}}(-k^{P_L(i+1)}ln(i+1)+E_{RX})\biggr]\Biggr]=\\

\displaystyle\Biggl[\displaystyle\biggl[P_0\tau \frac{1-(k^{P_L})^{i+1}}{1-k^{P_L}}+(i-1)E_{RX}\biggr] \cdot \displaystyle\biggl[ \frac{2[(1-k^{i+1})(k^{i+1}ln(i+1))-(1-k^i)(k^iln(i))]}{(1-k^{N+1})^2}\biggr]\Biggr]

</LateX Code>

I should solve it in k. I know it has at least a solution for k>1 (I used a graphical tool..) but I'm unable to find a closed expression of it even if I've managed in some way to simplify it (removing denominator and working on ln). I'm providing the full expression to let you start fresh.

If any of you can give a clue on how to get there I'd really appreciate that. I need to find an expression of k that holds for k>1 (with constraints if needed).

Have fun :-),

Lu