Can an employer trace an unknown number?

You probably should look for a new job because whether they can prove it or not they obviously know. They'll fire you for something else (made up if necessary) or scare you into admitting it by threatening legal action if you make them find out for themselves.

I'm guessing they can't legally find out the number without a court order and depending on the nature of your work that might well not be forthcoming; potentially that's some innocent customer's privacy being invaded. I wouldn't expect to be investigated like a criminal just cos I spent too long on the phone to customer services.

Why worry?

Stand up For yourself.

If there is no caller ID showing, NO

Service providers often have records of the actual phone number involved but they won't undertake a search of those records or reveal the information without a court order.  For what it's worth, an "unknown number" isn't entirely unknown, that's simply how it appears to the receiver.

yes,right back to you

EVERY phone number can be traced. Unknown Caller is just the callerID name.

It depends on what you're using to create the "Unknown Number" effect.  

This is from Century Link and it's quite correct. "Private numbers, blocked, and restricted calls can usually be traced. However, unknown, unavailable or out of area calls are not traceable because they don't contain the data needed for a successful trace."