Accidentally deleting an important email can be distressing. Thankfully most email systems will place deleted messages in a "Deleted" folder, much like the recycle bin on a desktop PC. However, once purged from the Deleted folder, these messages are much harder to retrieve. Depending on the email system you use, the Deleted folder may be purged automatically at regular intervals – however all is not necessarily lost.
Thankfully, if you're using Hotmail or Outlook.com you can sometimes recover accidentally deleted messages, even if they no longer appear in your "Deleted" folder.
To do this, look for the "recover deleted messages" option which will appear once you enter the "Deleted" folder.
Clicking on this will bring back as many deleted messages as possible and return them to the "Deleted" folder. From here you can move them to the folder of your choice.
If your important message isn't retrieved by this method then there's no more that can be done online.
If you're using a desktop email application such as Outlook Express, Windows Live Mail or Mozilla Thunderbird you can try data recovery software such as Piriform's Recuva which is a free data recovery program with specific support for retrieving lost emails. If you're using Thunderbird, you may also like to try the steps outlined here: How to recover deleted emails.