Solving an equation to find a function https://ift.tt/eA8V8J

I am trying to solve the following equation and find a real-valued function $y\left(x\right)$ which satisfies

$$ \exp{y\left(x\right)} + y\left(x\right) + 1 = 0, \hspace{0.2cm}\forall x>0 $$

The trivial solution $y\left(x\right) = x_0$ where $x_0$ is the root of $$ \exp{x} + x + 1 = 0 $$ is probably one solution. Is there any way to find a non-trivial one? Any ideas?

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George