As an engineer, my math knowledge is not rigour and I'm trying to solve the equation: $$ e^{-w}(w+1)=z $$ I know that it depends on the lambert function. But, I don't know how to get the equation above to the form in wikipedia.
I chucked into wolfram and get an answer. But, I have no idea where it comes.
My attempt so far have only been multiplying it by -1:$$ \Rightarrow(-we^{-w}-e^{-w})=-z $$
I'm not sure where to go from here. An explanation on how to solve this would be much appreciated.
$$\begin{align}e^{-w}(w+1)&=z\\-(w+1)e^{-w}&=-z\\-(w+1)e^{-(w+1)}&=-z\cdot e^{-1}\\-(w+1)&=W(-z/e)\\w&=-W(-z/e)-1\end{align}$$