I am going to be in the US for 100 days. As a european i am allowed by ESTA visa to be in the US during 90 days. For these extra 10 days is it possible to do an extension or to do another application through the ESTA visa without leaving the US?
The short answer is no, you cannot stay for 100 days using the ESTA and the Visa Waiver Program. You will have to apply for a visa or change your travel plans. The longer answer involves clearing up a lot of misunderstandings - primarily about what an ESTA (and the related VWP) is. See this question for a full description.
The ESTA does not allow you to remain in the US. It doesn't say anything about how long you can stay. It is a requirement for those wishing to enter under the Visa Waiver Program who are travelling to the US by airline or certain categories (eg Transatlantic cruise) of boat (not needed for those coming by land). Your ESTA is valid for 2 years (assuming you don't have a change of circumstances that would invalidate it). Not all Europeans (even EU Europeans) are eligible for the VWP/ESTA, incidentally.
On arriving by plane/cruise/whatever to the US, you will be considered for (you could always be denined) entry under the Visa Waiver Program. The VWP will normally admit you for up to 90 days. With regards to extending your stay, the FAQ on the offical VWP site says:
Persons admitted under the Visa Waiver Program are not permitted to extend their stays in the United States. See Extend Your Stay on the U.S. Citizenship and Immigration Services (USCIS) website. You must depart the United States on or before the date on your admission stamp when you entered the United States.
So, you'll need to apply for a Visitor Visa to the United States, and pay the appropriate fees etc. 100 days is a long time to stay and support yourself without working, so expect some questions about how you are able to do that. The website doesn't appear to say how long you can stay on each entry with a B1/B2 visa, so you may find that you have to extend your stay after you arrive - this is possible with a visa however, which it isn't with the VWP.