Isolating a variable that appears in the addend and exponent

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I am trying to rearrange the following equation containing variables 'y' and 'z' in terms of 'z = ...'

'a', 'b', and 'c' are known constants.

The equation is as follows:

$$ y = \frac{z + b(e^{-cz}-1)}{a} $$

My problem is that 'z' appears in both the addend and the exponent. Thanks for any help.