Solving a system of two equations for only real solutions

Question

I have a system of two equations

\begin{align} \frac{1}{2}A &= \frac{2.5 T}{\sqrt{-(\frac{\pi^{2}}{3} + 2\mu)}}, \\ \frac{1}{2}E &= \pi T + \frac{\mu}{2}A \end{align}

in which $A$ and $E$ are fixed. I want to obtain only the real solutions to this equation.

Solve[energy/2 == \[Pi]  T + \[Mu]/2 waveaction && 
  waveaction/2 == (5/2 T)/
   Sqrt[-(\[Pi]^2/3 + 2 \[Mu])], {T, \[Mu]}, Reals]

is my attempt to do that (where "waveaction" is the $A$ and "energy" is the $E$). The conditions given on the output are inequalities

What are those conditions for?

Answer 1

Click on the "+" in:

Then it will diplay:

Now click on "Uniconize". This will display the solution together with the conditions where the solution is valid. E.g.: