I'm having trouble proving the following using natural deduction:

(T > E) ^ (A > L) /... (T v A) > (E v L)

I checked the answer but I didn't quite understanding the reason why the proof progressed in a certain way (example, at some point the book used addition but I didn't understand why).

Would anyone mind walking me through this? Thank you!

The permitted rules are found here: https://www.cse.iitk.ac.in/users/cs365/2012/rulesLogic.html

The only exception is that absorption is not allowed and constructive dilemma is allowed (but I doubt that will apply to this case).