Dear {Name},
I owe all of you an apology for the email you received from me today. I have also reached out to apologize to {Name} personally.
I was venting to {Name} because I was upset in the moment about {situation} and I mistakenly hit "Reply All."
When I said {controversial thing}, I was being sincere, but it was not appropriate for me to take such a {rude/snide/demeaning/gossipy} tone, even in what I thought was a private message.
I'm not sure what, if anything, I can do to make this right other than apologize profusely. My personal disappointment in a situation should not have be be aired so publicly.
Sincerely,
{Name}
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