contend vs engage

contend

verb
  • To be in opposition; to contest; to dispute; to vie; to quarrel; to fight. 

  • To be in debate; to engage in discussion; to dispute; to argue. 

  • To believe (something is reasonable) and argue (for it); to advocate. 

  • To struggle or exert oneself to obtain or retain possession of, or to defend. 

  • contend with: To try to cope with a difficulty or problem. 

engage

verb
  • To enter into conflict with (an enemy). 

  • To come into gear with. 

  • To enter into (an activity), to participate (construed with in). 

  • To draw into conversation. 

  • To mesh or interlock (of machinery, especially a clutch). 

  • To attract, to please; (archaic) to fascinate or win over (someone). 

  • To guarantee or promise (to do something). 

  • To engross or hold the attention of; to keep busy or occupied. 

  • To arrange to employ or use (a worker, a space, etc.). 

  • To bind through legal or moral obligation (to do something, especially to marry) (usually in passive). 

  • To enter into battle. 

How often have the words contend and engage occurred in a corpus of books? (source: Google Ngram Viewer )