The third party that paid you is not your employer. You were an independent contractor, not an employee. That means you were in business for yourself, or self-employed. The third party is your customer, not your employer.
You enter the income as business income that was not reported on a 1099. You do not need the EIN.
The tag below your question says that you are using TurboTax Deluxe Online. You cannot enter self-employment income that was not reported on a 1099 in Deluxe Online. You will have to upgrade to Premium, or use any edition of the desktop TurboTax software.
