How to regrade an exam that was too difficult?
There isn't enough information here to really give good advice. You suggest the exam was too difficult. It may also be that it was invalid.  It may be that some of the questions were stated in such a way as to be misleading. There are measures of the validity of such exams, by the way. They measure the validity of a question by the proportion of students who answered it incorrectly compared to how those same students did overall. Some questions are negatively correlated with overall performance. 

Another issue is what your institution permits. Some have very strict rules about this. They are IMO unwarranted and counterproductive, but they may bind you. 

But absent such rules, you should care more about fairness than you do about numbers. To achieve fairness you may need to drop the exam or give an alternate. You may even want to rethink your overall grading scheme. 

One simple modification overall is to give course grades based on the, say, 8 best of 10 assignments/exams/whatever. Then the question of a poorly designed quiz never arises. Another way is to have quizzes every day so that no individual quiz is determinative of much of anything. 

However, some of the things that you might try will leave some students unsatisfied; especially the best students who worked the hardest. You can be kind to the strugglers, but not at the expense of the superstars. The situation is worst if the system itself puts the students in competition with one another for grades. Strict curve grading is IMO immoral as it makes it into a zero sum game where I can only advance at someone else's expense. If the system doesn't permit top marks for everyone (assuming it is deserved) then it is fatally flawed. 

Your purpose, I hope, is teaching, not grading. Use the exam as a teaching moment. Even have a class discussion about the questions that caused difficulty. Try to learn why people did poorly. Even permit different students to have different sorts of adjustments as needed. 

I used to have fairly strict rules about such things, but the understanding was always "This is the standard and you will do no worse than X if you do Y". And I always tried to make it an advantage to learn something even if was after the deadline or the exam. Make people want to learn, not just want to maximize points.