E-mail can be a difficult way to communicate with someone because you cannot see the person talking to you or hear the tone in their voice. Therefore, things can be taken out of context. When trying to resolve a problem or clear up a misunderstanding over e-mail, it is important to be articulate and use appropriate, strong words to express your thoughts. It is easy to confuse sarcasm with rudeness over the Internet, so reread your e-mail before sending it to the recipient.
Begin your e-mail with an apology. Apologise for perhaps overreacting or not sharing the message clearly. Show you want to make an effort to fix the miscommunication before things are beyond the point of fixing.
Use clear, precise language to explain your original point. Be sure you avoid using humour or sympathy; just directly explain what you originally wished to say. Using flowery language can cause further confusion and misunderstandings. In such a situation, it is important to take both responsibility and offer room for the other person to take some responsibility for the misunderstanding as well, but do this in a way without pointing fingers.
Ask the recipient if they wish to address any issues you did not see in the misunderstanding. Perhaps they can explain what they interpreted wrong, why they felt that way, and you can then use this information to avoid hurt feelings or confusion in the future.
Offer a way the two of you can resolve the issue, perhaps suggesting speaking about the matter over the phone or in person over coffee.