First, I’ll suggest taking a look at the Understanding Your INTJ Friend page. I’ve probably updated it since you initially asked this question.
As an ENTP, you have all opposite functions to an INTJ, which will naturally make it difficult for you to understand them. However, I have an INTP family member with whom I actually have a fantastic relationship, so it is possible for opposite types to get along.
The best advice I can give you comes from a principle I have lived by since I was a young teenager. If you want to get along with someone, you have to love them and to love them, you have to understand them.
In terms of MBTI, that means you should learn as much as you can about the way that your sibling’s thought process works (because it’s naturally going to work completely differently from yours).
One thing I should make crystal clear is the fact that even if you do everything you can to get along with your sibling, learn to love them and understand them –you cannot make them do the same for you (no matter their type).
I get along well with everyone in my family (that includes ISTJ, ESTJ, ENFP, INTP and ESFP), but they don’t necessarily get along with each other because while I’ve made an effort to smooth relations out with everyone I love, the people I love don’t necessarily make that same effort. The mere fact that they get along with me is mostly because I have made the effort. One of those five people doesn’t really get along with anyone except me in the family.
I tell you this only so that you don’t give up hope if your efforts don’t effect your sibling. Some people just don’t want to get along with other people, and you can’t change them. People have to change themselves –the only responsibility you have to any relationship is to try to understand and show kindness to the other party.
Ender Wiggin loved his brother, but did Peter ever really love him back? Not really, and it’s not Ender’s fault. Ender did everything (and more) to try to smooth things out with his brother, but ultimately, it was Peter’s choice as to whether he was going to love Ender.
Either way, just trying will make it easier to get along with your sibling, even if they don’t get along with you. In the end, patience is the key goal.