A few days ago, I sent an email to a party but they did not reply me and I cannot call them to confirm whether my mail was delivered or read by them. I am in a very high pressure situation, so I want to know whether my email is being delivered or not.
The short answer is "You can't".
The basic email protocol does not have any mechanism which requires acknowledgement of receipt built in to it, and once the email has left you, its no longer in your control, and (rightly imho), you do not get to dictate what can be done with it.
There are a few things which can be done which can confirm if an email has been read - however there is no requirement that the recipient do these things, so its a matter of "if they do these things you can confirm they have read it, but if they don't confirm, it does not mean they have not read it". These also require preparation BEFORE the email is sent, so won't help you unless you send another email (or did them before hand).
The first thing you can do is specify a "read receipt" request. When an email is opened it can send a notification to the sender confirming it has been read. Most applications will, however, prompt the recipient before sending t he confirmation. This mechanism uses the browser.
The alternative mechanism requires crafting an email with images (often, but not always a 1x1 clear pixel), with a unique name hosted on a web server. If and when the mail client opens the image, the web server can track that the image has been sent. This mechanism is often used by mailing lists - and, of-course, mail clients can be configured not to open off-site images or 1x1 images etc.
If you've already sent the message, you can't really know, until the recipient actually sends a reply. There is no way to peek into someone's inbox like that.
Email does have delivery receipts & read receipts, but they must be requested when sending the message, not after. (Plus, not all mail apps support requesting them – e.g. Outlook has this option, as does Thunderbird, but Gmail doesn't.)
It's not unreasonable to put your logo in the email and you can use the access to that rather than a suspicious looking 1 pixel extra payload
At the server side you need to perform a server redirect (eg via web.config on windows) so the request goes to your server application - just use something different for the url of the logo such as the email id in each email sent.
That way there is nothing abnormal at all to be seen at the client - but there are still issues
if the image is opened by an anti-abuse application looking perhaps for indecent images, then you are going to get a premature read report. If the anti spam software gets canny, it will pattern match out the signature in the email.
So you can up the odds of you knowing but never really know 100%
