Both of these verbs are used for asking about something or looking for information. The nouns for the request / investigation are enquiry and inquiry.

Technically, enquire is used for "ask" in general ("He enquired about prices for the products"), and inquire for a more formal investigation ("The police will make an inquiry into the alleged corruption.")

However, in American English it is now very common to use inquire for everything: "He inquired about prices for the products."

Fact
Warren G. Harding was the first American President to visit Canada. He stopped in Vancouver, British Columbia while he was on his way to Alaska.      .. More >>