The difference is not in their meaning but in the case. Einen is masculine in the accusative case while Einem is masculine and neuter in the dative case (see the link given above - http://german.about.com/library/blcase_sum.htm). If you need a refresher on the different cases, see this link -http://german.speak7.com/german_cases.htm
Can anyone verify if I have this sentence figured out? I would appreciate your help.
He plays with an animal. Er spielt mit einem Tier.
"He plays," Can stand on its own as a sentence and has no direct object....? "With" would be the conjunction? And, "Tier," must be the indirect object because there is no direct object of "plays?"
No, "with" is a preposition and in German it just happens to take the Dative case. Dative case is not just for indirect objects. "an animal" is the object of the preposition "with". Some prepositions require the Accusative case and those should be memorized. A very few prepositions take the Genitive case and should also be memorized. http://german.about.com/library/blcase_sum.htm http://german.about.com/library/blcase_dat.htm http://german.about.com/library/blcase_dat2.htm http://german.about.com/library/blcase_acc.htm http://german.about.com/library/blcase_acc2.htm http://german.about.com/library/blcase_gen.htm http://german.about.com/library/blcase_gen2.htm