I recently lost the back to an earring while at work. I made an emergency replacement, that has lasted several wearings now.
I cut a small piece from a wide rubber band—about 1/4-inch long, then pushed the hook of the earring through it snugging it to the back of my ear. It worked great and did not show. Maybe too great, because I keep forgetting to buy a proper replacement!
Pencil erasers work great for emergency earring backs too.