enquiry and inquiry - the difference
 
In the US, inquiry and enquiry are interchangeable, but be aware that many will consider enquiry to be a spelling mistake of inquiry.

In the UK, inquiry and enquiry are interchangeable. However, it is becoming preferable to use inquiry to denote an investigation, and enquiry to denote a question.
 

Enquiry and Inquiry

The nouns enquiry and inquiry can mean question, inquest, or investigation. They can be used interchangeably, but in the US, inquiry is the more widely accepted. The words enquiry and inquiry derive from the verbs to enquire and to inquire. (The guidance on this page relates to the verbs as well as the nouns.)

Not So Simple in the UK

In the UK, a distinction between enquiry and inquiry is developing. The word inquiry is being used in relation to a formal inquest (i.e., an investigation); whereas, enquiry is being used to denote the act of questioning. However, there is still notable leniency on this distinction. Of note, many in the US will consider enquiry a spelling mistake of inquiry.

Examples (UK convention):

I would like to enquire about the toilet facilities in the hotel.
(enquire = to ask)

The judge has suspended the inquiry into the police shooting of the escaped mental patient.
(inquiry = inquest or investigation)


See also:

What are adjectives?
What are nouns?
List of easily confused words