Yes it is Microsoft Outlook.com,I have tried logging in to webmail but unfortunately I am unable to.Is it a Microsoft email? Try logging into webmail to see if it's in the trash folder
There's a "deleted emails" folder. I guess you've checked that?
if they were deleted in 2013 they will be gone forever
if you only recently deleted them
go into the deleted folder - within the online outlook
you will then see the option to recover deleted