You can think of a function as some kind of machine that takes an input value, does something to it, and produces an output value. The inverse of a function flips the process around - you give it the output first, and it works in reverse to produce the original input.
The function [tex]\tan{\theta}[/tex] (θ being some angle) works the same way. It takes in an input angle, does something to it, and produces an output value. [tex]\tan^{-1}{x}[/tex], on the other hand, takes that output value and turns it back into that input angle.
So, with this problem, if [tex]\tan{\angle{T}}=x[/tex], feeding that x back into [tex]\tan^{-1}[/tex] would just get us the original angle back, or [tex]\tan^{-1}{x}=\angle{T}[/tex]
