Email can be used as a formal means to communicate, especially with time stamps. Email is however not unilaterally considered a respected forum to share course grades.
In the US, this lesson hinges tangentially if not primarily on guidelines from FERPA. In a nutshell, an instructor cannot share FERPA-level information such as course grades when he/she has no certifiable permission from the student to do so. This guideline is interpreted as limiting if not restricting entirely the use of email and even phone calls to give out course grades, sometimes even with a release from the student to waive FERPA restrictions.
When a FERPA-based policy is in place at an institution and when that prohibits a US instructor from sharing grades via email or the phone, the policy holds regardless of whether any policies exist that require instructors to share grades with a student. The latter question is addressed here. In the US, the general practice is that instructors should not/cannot prohibit students from valid requests to review their own graded submissions. Indeed, in the US, FERPA gives students the right to inspect and review their course records. Instructors may be allowed to set the manner of the review. By example, a university policy may be in place that allows instructors to hold the final exam for one year before releasing it back to the student. But the student should still be able to request a chance to review the final exam. The instructor may also be at liberty to prohibit such things as pen/paper or camera devices during the review.
Also, a FERPA-based institutional policy that prohibits instructors from sharing grades with students by email and an institutional or departmental policy stating that email is the only sanctioned method to correspond with students are not mutually exclusive. An instructor can be required to correspond with a student about official class policies only by institutional email (e.g. not by the university learning management system or by private email), but the instructor can also be cautioned about if not restricted from corresponding via any form of email with any student about the details of their performance in the course.
Policies with restrictions based on FERPA may not be in place at your institution, perhaps especially if your request originates somewhere other than from a university in the US.
In summary, you may need to determine whether instructors are or are not permitted to share grades via email. Ask at your university offices of academic affairs (starting perhaps through the offices of academic affair or the Provost for institutions in the US). You may also need determine whether your institution has a policy on how to request to review graded work (e.g. you may be required to file a written petition). Ask through the instructor or the departmental offices.
With all this said and done, and allowing for grace for the bluntness of the instructor, you might simply try asking the instructor for ...
Clarification on the policies to review your final exam and grades.
An office visit to review the final exam in person.
A video meeting where you present your university picture id to review your final exam "in person".