According to Roach (2004), the DRESS vowel is in between the cardinal vowels [e] and [ɛ] but closer to [ɛ] than [e]—so perhaps a precise transcription would be [ɛ̝].
The SQUARE vowel, however, is a falling centring diphthong and starts lower in the vowel space than DRESS—which one would transcribe as [ɛə̯].
For what it's worth, in other varieties of English such as Liverpool (Watson 2007) and Tyneside (Watt & Allen 2003), the SQUARE vowel is monophthongal, [eː] and [ɛː] respectively.
I can also testify, as a speaker of a non-RP variety of English from the North of England, that my DRESS [ɛ] and SQUARE [ɛː] vowels are the same quality and differentiated only by length (likewise, as it happens, for my KIT [ɪ] and NEAR [ɪː] vowels).
Roach, Peter. 2004. British English: Received Pronunciation. Journal of the International Phonetic Association, 34(2), 239–245. DOI: https://doi.org/10.1017/S0025100304001768.
Watson, Kevin. 2007. Liverpool English. Journal of the International Phonetic Association, 37(3), 351–360.
Watt, Dominic & William Allen. (2003). Tyneside English. Journal of the International Phonetic Association, 33(2), 267–271.