There is no Algebra I method to solve such things.

Have a look at Lambert's W-Function. This will suggest to you various methods that have been contemplated to deal with such structures.

Lambert W-Function -- from Wolfram MathWorld

Lambert W function - Wikipedia, the free encyclopedia

Lambert's W-Function

On the other hand, if you do not already know of the difficulty of solving what you attempted to solve, these discussions may not suggest much that you will find useful.

On still another hand, have you considered what happens as 'd' increases without bound? Does that lead to anything useful?

On yet another hand, after substituting and rearranging, we have

...and we can contemplate what happens for q = 0.