/t/ and /p/ are two phonemes of English: ten and pen are two different words. Replacing /e/ by /I/ result in [tIn] and [pIn], therefore /e/ and /I/ are also two phonemes, etcetera. In Dutch the /e./ as in [be.t] (beet) and /e:/ as in [be:r] (beer) are not two phonemes since they cannot distinguish two words: *[be:t] and *[be.r].
Phoneme is a structuralist concept of the smallest unit by which one can distinguish one word from another (e.g. Jacobson, Trubetzkoy). The phonemes of a language can be found by constructing minimal pairs.