If I were the editor and you posted my email, with or without my name, without my permission, that would be the last time I would ever have any kind of professional contact with you. I would be furious!
I would consider you untrustworthy and unprofessional if I found out that you have been sharing an email I sent you with even a limited number of your peers, but if you actually go as far as to announce it to everyone on social media, you would have burned all your bridges with me. I would never, ever want to work with you again under any circumstances.
Now, I may be a bit on the extreme end here, I know. I dislike social media so this feels particularly egregious to me. However, at its core, this is a case where you are taking confidential communication and blithely sharing it with the whole world! I can't imagine anyone would be OK with that. If you're willing to do this, how can I trust you not to share the information from the paper? How can I trust that you will respect the confidentiality of the review process? How can I trust you, period?
I get that you're excited to receive your first review invitation, I was too! And I shared the fact that I had been asked to review a paper with my friends. I did not share a confidential email though! So go ahead and share the fact that you have been asked to review. This is an important milestone and you should absolutely be proud of it! But don't ruin it by sharing the email, or anything else that can be used to guess who the reviewer of a paper may have been.
If you share the email, the best case scenario is that you will be perceived as immature and childish, and the worst case scenario is that you will be seen as someone who cannot be trusted.