Question: How to calculate the exponent of convergence of sequence of zeros of the function $f(z)=e^z+z$?

I know the formula (given below) to calculate the exponent of convergence but for this, I need to know the zeros of the function explicitly, which I don't know. I found in the literature that the exponent of convergence of sequence of zeros of the function $f$ is 1, but I can't understand how it is so.

The exponent of convergence is given by $$ \lambda(f)=\inf \left\{p\geq 0:\sum_{i=1}^{\infty}\frac{1}{|a_i|^p}<\infty\right\} $$ where $a_i$ are the zeros of $f$.

Can someone help me to understand how shall I proceed?