You can check that things in two different ways like, by using the header "Disposition-Notification-To" to your mail function, it will not going to work in all case because most people choose not to send read receipts. If you could, from your server, influence whether or not this happened, a spammer could easily identify active and inactive email addresses quite easily.
You can set header like
$email_header .= "Disposition-Notification-To: $from";
$email_header .= "X-Confirm-Reading-To: $from";
now the another method to check is by placing an image and you can add a script to onload of that image, that script will send notification to your system that xxx user have read the mail so, in that way you can track delivery status of the mail.
In fact, I can't think of any way to confirm it's been delivered without also checking it gets read, either by including a image that is requested from your server and logged as having been accessed, or a link that the user must visit to see the full content of the message.
Neither are guaranteed (not all email clients will display images or use HTML) and not all 'delivered' messages will be read.
Though for more info https://en.wikipedia.org/wiki/Email_tracking