Update: Since around January 2018, it is now possible to search using the email parameter on Stripe. See the accepted answer.
I
Since you specified that
The documentation only indicate to search by created, ending_before, limit and starting_after, but no "email".
You are right, you can't search using emails.
If you still wish to do that, What you can do instead is to get a list of all the customer and filter on the response you get using email.
For Example, in ruby you can do it as follows:
customers = Stripe::Customer.all
customer_i_need = customers.select do |c|
c.email == "foo@bar.com"
end
PS: Stripe can have multiple customers associated with one email address.