engage vs engagement

engage is not a noun while engagement is a noun.

Word	Noun	Adjective	Verb	Adverb
engage	No	No	Yes	No
engagement	Yes	No	No	No

engage (noun)	engagement (noun)
	the act of sharing in the activities of a group
	a hostile meeting of opposing military forces in the course of a war
	the act of giving someone a job
	employment for performers or performing groups that lasts for a limited period of time
	a mutual promise to marry
	contact by fitting together
	a meeting arranged in advance

engage (verb)	engagement (verb)
get caught
consume all of one's attention or time
give to in marriage
keep engaged
engage for service under a term of contract
hire for work or assistance
ask to represent; of legal counsel
engage or hire for work
carry out or participate in an activity; be involved in
carry on (wars, battles, or campaigns)