Had the misfortune of experiencing of doing the Apple equivalent of bricking my iPhone while doing an iOS update.  Why did I do an iOS update?  Well here's how I did this without any data loss. 

Because iTunes apparently, wasn't doing any backups of it.  Thinking the latest iOS update would fix that, I proceeded to try the upgrade on my phone when I had 58GB / 64GB used up. 

Unfortunately, it didn't go so well:

The iPhone "iPhone" could not be restored. An unknown error occurred (14). 

A subsequent update wouldn't fix that.  Multiple calls to Apple Support didn't yield much more then what I already tried:

• Try to use another cable.
• Update from another laptop.  Used a MAC Book.  No luck.  Same iTunes error as above.
• Tried to read about the code. No luck.  
• Tried to exit recovery mode through some apps.
• Tried various apps available online to attempt to troubleshoot.  No luck.  Didn't try to update the iOS using those apps.  I didn't go that far. I'll only trust Apple products to do so. 
• No apparent backups were listed in iTunes. 

Visited an Apple Support suggested retailer but was advised at that store that if an update could not be done, an expensive data restore would need to be done if I'm to retrieve anything off my phone.  However, a charge of about $1000 came with that. So one more call to Apple clearly showed I've no options except to restore and lose all 58GB of my data.  Ouch!

It is what it is.  I proceeded to start the Restore steps.  The phone was overwritten.  Then to my surprise, I see this screen:

 

So there is a backup?  Interesting how this backup is nowhere to be seen or verified in iTunes for Windows 10.  Doesn't matter, it's here and I could use it.  Despite this, I'm not confident everything was there so I let the process estimate the time.  Once it confirmed it would take About an hour, I felt better that all my files will be there.  Sure enough, after setting up the passwords and verifying some initial settings after a restore, everything is back to the way it was, including the 58GB of videos and images:

Freedom indeed!  Hope this helps everyone else here too. 

Cheers,
TK