engage vs engross

engage and engross both are verbs.

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

As verbs, engage and engross are synonyms defined as:

Other synonyms of engage include absorb, occupy.

engage (verb)	engross (verb)
get caught	consume all of one's attention or time
consume all of one's attention or time	devote (oneself) fully to
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)