If you did not organize as an LLC or something else, your business income and expenses are listed on a form called Schedule C that is attached to the rest of your tax return, and your profit from schedule C flows to your form 1040 where it is combined with your other income (wages, gambling, pension, etc) and your personal deductions, to calculate your overall tax.
If you have an EIN, you will include that on your schedule C. The IRS won't be confused because the EIN is linked to your SSN. Having an EIN is good practice, because it means you don't have to give your personal SSN to vendors or clients.
