Is it possible to solve this equation using lambert function Can the following equation be solved using Lambert function?
$$x(1+e^x)=a$$
 A: No. Lambert's W function  solves only cases of the form $~xe^x=$ constant, whereas here we have $xe^x=$ variable.
A: We know that mixed exponential/bilinear equations can be solved by the extended Lambert function $W_r(x)$, which can be represented by the following Lagrange inverting series:
$$z(A,t,s)=t- (t-s) \sum_{n=1} \frac{L_n' (n(t-s))}{n} e^{-nt} A^n$$
which is the solution of:
$$e^z=A\frac{z-t}{z-s}$$
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References
On the generalization of the Lambert $W$ function with applications in theoretical physics, http://arxiv.org/abs/1408.3999
[68] C. E. Siewert and E. E. Burniston, "Solutions of the Equation $ze^z=a(z+b)$," Journal of Mathematical Analysis and Applications, 46 (1974) 329-337. http://www4.ncsu.edu/~ces/pdfversions/68.pdf
