If you are referring to the EIN in the US, I have seen that wording/acronym used in places where they actually wanted the company's Federal Tax ID which is obtained from the IRS, I believe.
Indeed, the IRS are the ones that assign the EIN. Now, as far as I've heard, it can be quite a complex and tedious process. The main thing is if your oversea company will have a physical location in the US or not. At the very least, regardless of location, you need to open a bank account. So far so good, here comes the tricky part. To obtain the EIN, you need to provide the Social Security Number (SSN) of a "principal officer". As this was a very broad term, open to various loopholes, it was later defined as "someone who controls, manages, or directs the corporation and the disposition of its funds and assets". This was changed to prevent companies without an office in the US to temporarily assign someone with an SSN as "vice president of something-something" just to use him for the EIN. This was modified to avoid the cases of tax non-compliance. In short, if you do have an office in the US also, it shouldn't be such a hassle to get an EIN, otherwize prepare your nerves of steel, as you're gonna need them