problem vs enigma

problem and enigma both are nouns.

Word	Noun	Adjective	Verb	Adverb
problem	Yes	No	No	No
enigma	Yes	No	No	No

As nouns, enigma is a hyponym of problem; that is, enigma is a word with a more specific, narrower meaning than problem:

problem (noun)	enigma (noun)
a source of difficulty	something that baffles understanding and cannot be explained
a question raised for consideration or solution	a difficult problem
a state of difficulty that needs to be resolved