I always had this confusion since childhood over inquiry and enquiry. My memory failed me and hence I forgot to ask Mr. Robert Watt, Sheru di and Mrs.Moitra (my favorite teachers who taught me English). May be I did ask. Don’t remember, my memory fails me anyways I still seem confused over it’s difference. So I googled and got this:

The en- prefix derives from French, whereas the in- form comes from Latin.

Enquiry and inquiry do not mean exactly the same thing.

Some organizations such as newspapers tend to prefer the in- form, but a distinction should be made between, for example, an official inquiry and an informal enquiry.

For example, a journalist will ring a PR professional and make an enquiry about a topic. Enquiry is used when asking a question or seeking information.

Inquiry is for official investigations (analysis, investigations, post mortem, etc). i.e. The senate will hold an inquiry into fuel prices.