"¡Enséñame el mundo!"
Traducción:Zeige mir die Welt!
I have the feeling both is possible in spoken as well as in written language. I am person, who preferes 'zeige', "Zeige mir deine Hände!" and "Zeig her!". In all longer sentences I like to use the 'e' in the end. (I think it sounds softer and warmer with the 'e'.)