I'd probably test it with two regexes. First check for one (e.g. is it a valid email), then if that fails, check it with the other (e.g. is it a valid phone number). If neither, show a validation message saying that the value is invalid. I won't supply regex examples here as there are dozens of those around the internet and each has pros and cons - no sense starting a flame war over the best regex for email or phone, but the code would look like the following:
function validateEmailPhoneInput(field)
{
if (emailRegex.test(field.value))
{
//it's an email address
}
else if (phoneRegex.test(field.value))
{
//it's a phone number
}
else
{
//display your message or highlight your field or whatever.
field.classList.add('invalid');
}
}