"either of two ways" is correct and usable in written English.
You can use it when referring to two different options or approaches. For example: We can complete the project either of two ways - by doing it ourselves or by hiring a contractor.
When culture is challenged in this way, and people start questioning what their organization stands for, things can go either of two ways.
Being with someone who remains in love or attached to another person can go either of two ways - one, it can lose your current date very fast or two, it can cause your current date's own insecurities to surface and rebound on you, to the point where your date constantly seeks your reassurance.
Now this may come about in either of two ways.
This can happen in either of two ways.
Sticky files can be deleted in either of two ways.
Safety glass may be made in either of two ways.
2016 could either go one of two ways for MLS's shiniest club, with Bruce Arena leading a revamp of his squad in the post-Landon Donovan age.
It can either go one of two ways: pull together and make new cemeteries, or readjust the way we think of what happens to us when we go, whether it be cremation or whatever.
This may happen in either or both of two ways: by changing the importance of courtship mating relative to sneak copulation as a determinant of sexual selection, and by changing the strength of sexual selection imposed by choice.
A Pisces/Pisces love match could either go one of two ways: unburdened and complete love for one another, or consummate distaste.
This can be done in either one of two ways: the forward mode or the reverse mode of automatic differentiation.
