I need to solve following equation for $w_1$:
$$\mu=\frac{w_2}{w_1+w_2}\times\left(1-e^{-(w_1+w_2)t}\right)\times N$$ when i use matlab solver to solve this eqution for $w_1$, the result is as follows: $$w_1=\frac{2\times t\times w_2 +\mu \times lambertw \left(0,-\frac{exp \left(\frac{-(2\times t \times w_2)}{\mu}\right)}{\mu}-\mu \times t\times w_2\right)}{\mu \times t}$$ my question is, what is exactly lambertw function and how can i evaluate above equation to find $w_1$ for specific $w_2$, $t$ and $\mu$? for example if $w_2=0.5$, $t=10$ and $\mu=20$, what is $w_1$? (Of course not using the matlab or other softwares)
Update:
i need to use above function in my java code. So, i cant use other softwares to evaluate it for specific values.
