Dear {Name},
I wanted to let you know as soon as I realized it: I made a mistake on {assignment/project}. I am so sorry. I realize now that I {misunderstood/cut corners/acted outside of my authority/etc.}.
In order to fix this, I'll need the help of {you/boss/team/coworker}. Please let me know when we can meet to discuss the next steps.
Again, I apologize for putting you and the company in this position.
Sincerely,
{Name}
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Index of letter of apology templates