I decided to use the Maple software to help me solve dynamic optimization problems, and I found this final solution for T. (example in the picture). example
What does the LambertW mean for the solution T? Can I get rid of this expression to express T in simple terms? Does theLambertW (including the expression inside it) have a solution or an equivalent expression? If this is the final form, I assume I can no longer proceed with symbolic/analytical solution, and I must move to computation?
Computer algebra software gives your solution in terms of Lambert W if it hasn't found solutions in the elemenary functions.
It depends on your objectives if you accept Lambert W as closed form.
You can use the algebraic properties (e.g. transformation rules and special values) of your closed-form solution/Lambert W.
On the other hand, a closed-form expression is a placeholder for its analytic representations (Wikipedia: Closed-form expression - Analytic expression), e.g. its series representations, what can help to find approximate numerical solutions/values much easier in some cases.
Lambert W solution holds for your general parametric problem. Maybe there are some elementary solutions for some special properties/values of your parameters/constants.
Your equation cannot be rearranged by applying only elementary functions if it is an irreducible algebraic equation of more than one algebraically independent monomials.
But if your equation has solutions that are elementary numbers is a different mathematical problem.
