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."
This 23acre public botanical garden is home to a conservatory and a variety of themed gardens. The Gardens feature North Americas largest collection of plants from cold temperature climates around the world, as well as seven diverse gardens that mostly include plants from Colorado state.