As a flock they do lay a variety of different colors but not each individual EE hen. Each hen has a color she lays and she's always going to lay that color. Either she has the genes to make a color of pigment or she doesn't. There might be some variation in shade so that sometimes a blue laying hen has a pale blue egg or sometimes its a deeper blue. Especially in a new layer that is still working out her system. But for the most part her eggs are all going to look pretty similar from day to day. It is possible for there to be some problem in the egg production and the pigment does not get applied so a hen that lays brown eggs could possibly lay a non-pigmented white egg, This is not normal though and not that common.
I have 5 EE hens. One lays a blueish egg, three lay olive eggs, one of which is a darker olive almost brown, and one a very very pale brown that almost looks white or pale pink. I've watched the hens enough that I have a pretty good idea which hen lays which color and when I see one in the nest box I know even before looking what color it's going to be.
Barred rocks lay brown eggs often with pink tones so I bet the brownish pink egg is from her. Don't know what breed your "brown" chickens are but is it possible one of then is also an EE? EE are mutts that can include a lot of other breeds and thus can have lots of variation in looks and colors. They can also vary quite a bit in egg production. High production stains might give you an egg every day but lots are breed to more dual-purpose/heritage chickens and thus will give you eggs slightly less often, Maybe 4-5 egg a week rather than 7. Barred rocks are heritage breeds that are more likely to lay 4 or so eggs a week not every day. Lower light levels and colder temps in winter can also decrease egg production. So 3 eggs from 4 chickens is probably about what you should expect. I get 2-4 eggs each day from my 5 EE hens.
