Solving an equation with both linear and exponential terms

Question

Can I find an algebraic solution for the equation below? Thank you.

$$ x+e^{x}(x+a)=b $$

Answer 1

The equation $x + e^x (x + a) = b$ is transcendental, and, unfortunately, in this case there is no closed formula for $x$. This equation can be written as $$e^x = \frac{b - x}{x + a},$$ so it should be clear that one cannot solve it analytically.

Answer 2

As already said by other comments and answers, the equation is transcendental and there is no closed formula for the solution. Only numerical methods (such as Newton) would provide a solution.

By the way, the equation can look "nicer" if you define $x+a=y$.