The question is too difficult for everyone to answer.
The question is too difficult to answer.
Do the above two sentences mean same? or there is a difference between the two?
The first sentence is rather ambiguous, and would probably not get used much. It is ambiguous since it can mean "Not everyone can answer (but some can)" or "Everyone is unable to answer (ie nobody can)" You probably meant to ask about "This question is too difficult for anyone to answer."
The context of the second sentence could change its interpretation. If you are a student it would probably mean "too difficult for me to answer". If you are a teacher it could mean "too difficult for my students to answer."
So there may be cases when using "anyone" adds information, and the two sentences are not exactly the same.