Can you explain the symbols in the equation?
That cannot be solved in terms of elementary functions. You can do this:
Let u= T+ E. Then E= u- T so and
The equation is now or .
Now, let v= u/T so that u= TV. The equation becomes or .
Now you can use "Lambert's W function" which is defined as the inverse to the function
Then .
Then, of course, and .