In Spanish there are only five vowels: a,e,i,o,u so no "two 'e' pronunciations", it should be the same all the time.
Note however that Spanish is just one of the languages spoken in Spain. There are four different cultures: Catalan, Galizian, Basque and Spanish, each one with its own language, and even dialects too.
Some of these languages have different "sounds", for example, in Catalan (spoken in Catalonia, Valencia and the Balearic Islands) there are eight vowels: a, open e, closed e, neutral e, i, open o, closed o and u. Thus, a native Catalan speaker speaking in Spanish might pronounce e's and o's differently from a native Spanish speaker.
Same goes with, for example, Galizia -where they speak "galego"-... they have seven vowels, and it so happens Madrid if full of residents originally from Galizia, so you might find some "madrileños" that pronounce Spanish rather different from the autochthonous die-hards, so to speak.
Important: for political and historical reasons, language has always been a very delicate subject in this neck of the woods, so make sure you understand that the languages mentioned above are languages on its own right and not dialects or sub-divisions of Spanish so to avoid upsetting locals (and also looking like a fool) if mentioned in a conversation
Aaaanyhow.... regarding Spanish: contrary to some other languages (ie Russian) where a slight variation in pronunciation might yield a completely different meaning or some others (you know who you are!) where native speakers are rather "snooty" --and if you, as a foreigner, don't pronounce "exactly as it's supposed to be" they frown upon you claiming they don't understand--, Spanish is quite flexible and Spanish speakers quite understanding when a non-native speaks this language. What I mean is that you'll be "understood" even if you don't nail it when pronouncing a word.