My guess is that your friend probably hasn’t said anything because she doesn’t realize you’re upset. You say that she asked to “rent” the camera, which seems less like a personal favor between friends and more like a business arrangement between acquaintances. And if she’s renting a camera from you, it sounds as if she isn’t hiring a professional photographer and is working with a limited budget—which might mean that the guest list is small, and that you aren’t part of a tighter inner circle that would be included on that list.
In other words, there might be a mismatch between her idea and yours about the nature of your friendship. Maybe to her, you two are friends, but not close enough for her to include you in her wedding celebration—or even close enough for her to ask to borrow rather than rent the camera. It’s highly unlikely that she’d have asked for the camera if she knew that you would be hurt if you weren’t invited to the wedding. She probably assumed that you didn’t expect to be there.
What could be most hurtful here, then, isn’t so much the not being invited but what it implies: that she doesn’t consider you to be as important to her as you’d imagined. In your mind, of course you’d be at her wedding (camera or no camera); in her mind, you’re a friend she enjoys but not one who’s close enough to get a wedding invite. Your situation reminds me of a person who lands in my office after discovering that while she believed that she and her boyfriend were going to get married, her boyfriend had no such intention. In those cases, I help her to look at what led to such a gap between their respective understandings of the relationship. Sometimes a person willfully ignores information she doesn’t want to have and signs she doesn’t want to see; sometimes she invents a story in her mind based on her hopes; and sometimes these misunderstandings repeat themselves in other relationships, leaving her baffled as to why other people would (in her view) treat her so poorly.
The only way to possibly understand what’s going on here—not just with the wedding invitation, but more generally in the friendship—is to ask. I say “possibly” because your friend may not be completely transparent, so as to spare your feelings or avoid an awkward encounter. But if you really have the kind of friendship in which you’d expect a wedding invitation, you should be able to talk to her about this.
Before you broach the topic, though, it’s important to adjust your goal for the conversation. The aim should be to understand more about your friendship, not to accuse her of having done anything wrong or pressure her to say something she doesn’t feel. You might say, “Hey, I’m thrilled that you’re engaged and I’m happy to rent my camera to you. I know this might be uncomfortable to talk about but we’ve been friends for X number of years, and when you asked to rent my camera, I assumed I’d be there to celebrate with you. I’m not asking for an invitation at this point, just a better understanding of what’s going on between us.”