Read this really interesting piece on fivethirtyeight recently about what happens when you get promoted but your friend does not. The authors conducted a survey, and not surprisingly found that most people think that the two people should "talk it out."
Ok, but what does that mean?
If you have one person that is seriously jealous in this situation, then "talking it out" could go quite badly, especially if those emotions are still quite raw. Talking it out could quickly become "yelling it out" - this could do permanent damage to the relationship.
Yes, the two people need to discuss the problem, but only when the person who was passed up for the promotion is ready. That is, can he or she talk to the promoted individual without feeling the pangs of jealousy and anger. What may be helpful for the promoted individual is to deflect the situation to the manager or the company.
"So, I had an interesting conversation with [manager] after these last performance reviews, would you like to chat about it?"
...is much less threatening than:
"You seem upset with me. Do you want to talk about why I was promoted and you weren't?"
Being promoted doesn't mean the end of the relationship as look as you figure out the right way to "talk it out."