First, as a matter of style, I would avoid using i.e. and e.g. altogether. These are Latin abbreviations whose actual meaning is lost on most native English speakers and almost all readers coming from another native language.
Second, they have similar meaning, but are not equivalent. See http://public.wsu.edu/~brians/errors/e.g.html for a concise explanation.
Third, writers typically mean "for example" or "such as" when they use e.g. and i.e. Better IMHO to simply write what you mean and be done with it.
To answer the original question: in your last example, the answer is simple. Using e.g. or i.e. would be unnecessary and possibly grammatically incorrect in this construction. The passage is perfectly clear as:
"As we discussed, you will bring two items. (A sleeping bag and a tent are not optional.)"
Note that the period goes inside the parentheses. It does not add any information, though it is not incorrect, to say:
"As we discussed, you will bring two items. (For example, a sleeping bag and a tent are not optional.)"
"As we discussed, you will bring two items. (That is, a sleeping bag and a tent are not optional.)"
All that said, if either e.g. or i.e. begins a sentence, it should be capitalized.