The words inquire and enquire are basically synonyms meaning to ask for information. That is to say that they mean the same thing, but are often used in different situations.
Enquire: to ask
Inquire: to ask, but used more for making a formal request
Enquire is also more common in British English, while you will find Inquire being used more in American English. Generally speaking, it doesn’t matter which you use in your everyday communication.