Yes, of course, anyone can apply for visas with the U.S. government without professional assistance. However, applying for an E-2 Visa requires more than just completing an application and can be complicated.
In order to save money and time, it is advisable to hire a qualified US Business immigration attorney to do your applicant and a US Business Immigration consultancy firm to present your business (commonly named business plan) the right way to USCIS.
Overall, these firms will produce a complete E-2 application packet that meets the government requirements and increases your chances of approval.