We start with the given statement. Then we use the segment addition postulate like so:
QT = SU
QR+RS+ST = ST+TU
QR+RS = TU
QS = TU
in the second step, I broke up QT into QR+RS+ST. Basically segment QT is composed of the smaller pieces QR, RS and ST. Similarly, SU is made of ST and TU.
The third step has us subtract ST from both sides.
Lastly, we combine QR+RS back into QS to conclude the proof. You could argue that QT = QS+ST and avoid this step if you wanted. It's up to you how you want to approach the proof.