'E(q)' suggests elasticity of demand, which suggests your derivative quotient is upside down:

So you do want to solve for dq/dp after differentiating implicitly. Have you done that?Originally Posted bythe above wiki page under 'point-price elasticity'

Spoiler:

Then you have E(q) in terms of p and q, i.e. for any particular point on the demand/price curve.

So, not sure why you want to solve for q. But if I've mis-read, please explain / supply more detail.

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