Received a mail from 10.142.208.5, private IP. Need to know the location details

Not a hope as this address range is PRIVATE, as you have already found.
That means it is used all over the place by many companies for internal networking.

There are a couple of other reserved ranges for private use, namely 172.x.x.x and 192.168.x.x

That is just one of the addresses. If you reader the header of the mail, you should find other addresses. The one after that one will go further up in the network. That number is one of a private internal network.