Maybe it's an ETIN you're running across.  If so, that's the Transmitters number.  When sending an e-file to the IRS through a software program, that program acts as the Transmitter.

IRS issues "tracking numbers" on your efin documentation (Application Summary) which may be what you're referring to, but TAXOH is correct, the EFIN is your main concern.  

I have already have an EFIN number, but I am told that for the 2018 filing season, a "tracking number" will be required by IRS to be able to e-file.

Have you searched IRS website re: this "tracking number"? An EFIN is what one needs to efile which you state you already have. You are not talking about a "submission id #" are you?

I think the e-file also records the MachineID which is specific to the computer the file is generated from. This is not new for 2018. Whatever it is, I am sure we all have one so that IRS can chase down all the bad guys that are filing fraudulent returns. I you are one of the good guys, don't worry about it. 

Each return used to have DCN (Document Control Number) a few years ago that became the Submission ID. https://www.irs.gov/e-file-providers/ero-duties-after-submitting-the-return-to-the-irs