Dear {Name},
I hope you will accept my apology for being curt with you. My nerves were fried due to {situation}, and I took it out on you when you were simply {doing your job/asking a question}.
What I should have said was {alternate response}.
Please don't let my rudeness affect how we interact in the future. I truly respect your {position/role/curiosity}.
Sincerely,
{Name}
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Index of letter of apology templates