This is rather simple. According to Grammar Girl, each other is always two words in English. The AP Stylebook further explains each other and one another, where more confusion occurs.
As quoted from the 2007 AP Stylebook “Two people look at each other. More than two look at one another. Either phrase may be used when the number is indefinite: We help each other. We help one another.”
To sum it up, eachother is not a word in English. Each other and one another depend on the number of people involved.
Clear as mud?
Well to-day was once two words. I believe the separation of each and other will look foriegn to the kids of the future, as to-day looks to-day. Each other represents a singular idea, and because of this we say it as one idea. We no longer pause between the two words, and therefore are hesitant to write it differently. We now say today as a combo, but before it was combined it must have been spoken as to-day.
Good to know! Thanks, Natalie!
Aurora