The e-mail address isn't included in the actual message sent by the Contact Form initially, so it's very likely you will think the e-mail isn't included at all.
You can find it by clicking on the "Reply" button on your mail client. In the below screenshot, I'm using Thunderbird and you can see that the e-mail of the sender appears already filled-in, in the "To:" field.
There are some cases when the e-mail doesn't show up this way and it means that your mail server isn't configured properly, because the e-mail is removed.
That can be easily fixed, you can go to your Contact Form module, open its settings and, in the "E-mail" sub-section, find the Message Pattern option:
You can customize the message you get from the Contact Form and include all the details you want, in any format. By default it will only send the message, but you can adjust it to say something like:
Please note that the fields can be referenced by using %% before and after the actual ID of the field:
For the e-mail field it should be referenced as %%Email%%.