Maybe it's too late to respond to this post, but maybe it will still help.

1. (F∨E)→~D
2. S∨D
3. E ∴ S


Translation --
Step 1: It is possible that when either F or E (or both) are actual, then D is not actual.
Step 2: It's now true that either S or D (or both) are actual.
Step 3: It is now true that E is actual. Therefore, it is also now true that S is actual.


Why is it now true that S is actual?
(i) To start, E is now actual. Which means that D is not actual, because of step 1.
(ii) In step 2, S is the only thing that can be actual because it step 2 says that at least one of the two must be actual. And since D is ruled out as being actual in step 1, the only thing that remains is S.
(iii) That is why the conclusion is that since it's now true that E is actual, it is true that S is actual.


Of course, these logical proofs are not entirely conclusive, so long as we have an non-exhaustive or irrelevant set of premises. The conclusion only holds if the premises are not only accurate and relevant, but also exhaustive. Presumably, the only sort of conclusion that we can have is about ourselves, since that, at least, has the real potential to be complete, accurate, and entirely relevant.

PS - by "actual," I mean "actually true." And by "potential," I mean something like "potentially true."