@oliverr:
It is only possible to use phpMail
I'm not sure exactly what kind of restriction this is. Is outgoing mail blocked? Are you limited to the PHP libraries they provide?
(Maybe there are better choices for hosting BTW)
Also, how are you trying to email? Did you create a form? Details are always welcome as it becomes very tedious asking back and forth on this kind of platform.
I suggest you use a third party mailer service like Mailjet (free) or Purelymail (paid but v. cheap).
If outgoing email is blocked completely from your host, the Email plugin from version 4 lets you use the APIs of third party mailers. You need to use a separate plugin for each API (e.g. Sendgrid's). Using the API means that you are generating email through a web service they provide, so no mail protocols or libraries are used on your host. This should work around any email restrictions they have.