well pump pumping water into tank continuously

I'm new., and have no experience with well pumps., and really need some advice.
I have a well tank that sounds as if it is continuously filling. The only time I hear it shut off, if the toilet upstairs is flushed.
The pressure on the tank says 40. It is not easy to read. I purchased this house 3 years ago., the tank seems as if it is not that old. It is in good shape and quite clean. I'm afraid this will burn out my well pump.
I have called my plumber and its toward then end of the afternoon and it is still running . Is this something of an emergency.
I'm also do to go on vacation at the end of the week for a few days., and really don't want to leave this running like this.
The well is about 10 years old. We are not sure how deep the well is., and I know this information is probably not as complete as you need, and I'm sorry, wish I knew more about this department.
Can you offer any help to what this could be?
If this is any help., we had the switch changed about a year ago when there was no water coming in the house.

The tank is not what is running, it's probably the pump and if it's running steady without moving water it will certainly burn up. Turn if off until someone comes to work on it.

bob...