Conditional sentence type 2 means that condition is unreal (unlikely to happen) and it refers to the present or to the future.
Sigh. It's sentences like this that make those of us who study English grammar wish that people would stop teaching the "1st, 2nd, 3rd etc conditionals".
Your teachers have apparently never told you that the construction with a past construction in the condition clause and would VERB in the consequence clause does not necessarily indicate an "unreal" (that is, counterfactual) condition. (In fact one authority, Conditionals: A Comprehensive Empirical Analysis by Declerck and Reed, distinguishes eight different uses for this construction!)
If I found her address, I would send her an invitation.
This sentence does not express a present counterfactual: a promise of a future action (send her an invitation) contingent on a future possibility (find her address) may be 'non-factual' or 'not-yet-factual' but cannot be counterfactual
The most likely interpretation of this sentence is that it expresses a contingency and a consequence which were prospectively possible in the past. Its most likely context is a narrative in which it acts as exactly the indirect-speech report which you're looking for:
I told him I'd do all I could: if I found her address I would send her an invitation.
(It's also possible that it means "I made a habit of sending her an invitation on every occasion when I found her address"—but that's such an odd thing to say that it doesn't seem very likely.)