IPhone 5s :: Recover Number From Memory Without Backup?

An individual gave me their phone number, so I dialed it and waited until I saw it go through on their phone and hung up. The next day I accidentally deleted the phone number. When I went to my cell provider's website to check my call history and get the number it didn't show up. I've tried doing a number restores from the phone's memory but nothing is showing up. I didn't know if there was a way to recover this number at all or if all is lost. I know the exact time and date of when the call was made and am desperate to be able to recover this number. I would really love to recover this number! I'm working with an iPhone 5s.