If you are installing 10 on the new machine solely for the sake of installing 11, you do not need to. You will only need the serial number from 10 to install 11 if 11 was purchased as an upgrade.
If you want to uninstall 10, there should be a deactivate option in the help menu that you should use before uninstalling. If you have a disc for 10 you can use that to install it on the new machine. If not, then you can download the trial version of 10 from the page linked below if you follow the Very Important Instructions. You can use your current serial number for 10 to actvate it on the new machine.