Here's those two characters together for comparison. It took me a while to figure out what you were talking about because the two render so closely in smaller text.
Interestingly enough, searching for ě on the page finds the ĕ as well, but so does search for e...
At least in Firefox the search pane has a ‘Match Diacritics’ option. Turning it on causes it to match only the precise characters in the textbox. (It’s slightly misnamed, since it doesn’t just handle diacritics, but also cases like ⟨e⟩ vs ⟨ɛ⟩.)