I have a question regarding solving an equation in Mathematica. I want to find the functions of p and T from the equation shown in the attached image in order to determine the optimal solution(p and T is the decision variable) 
The example of function of decision variable that I want to obtained is like this (i took this example from another paper): 
Based on some papers I've read, to obtain the functions of p and T, I need to differentiate TP with respect to p and T first and then try to get the function of p and T from the resulting equations manually. Is there a way to obtain these functions directly in Mathematica?
I have tried using Solve and NSolve, which worked for simpler equations, but for my equation, I keep encountering errors like 'Solve::nsmet: This system cannot be solved with the methods available to Solve.' Today, I retried it, but Mathematica got stuck running for a long time. Is there anything I could do?
Any advice or solutions would be greatly appreciated. Thank you!
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