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I am looking forward to hearing from you soon is also correct but less formal. It has kind of the same meaning as you would have said "I really look forward to hearing from you soon" and since expressing emotions is not considered very formal we don't use them in formal writings.
Thank you!
can any body please correct this text.. it is to acquire about the job application process

Dear first and last name,

I hope you are doing fine.

I was wondering if I could take your few minutes to ask about my job application status as "Trainee".

I would be glad to share more information if required.

I look forward to hearing from you soon.

Best Regards

first and last name
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'I am looking forward to hearing from you soon' - incorrect
why is the above sentence wrong?
Correct, it is a phrasal verb in its cont form.
Hi, I think I'm looking forward to hearing from you is formal.

Emotion: smile Bye(P.S from a 5th grader) LOL
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