Are any differences between two sentences?
I can handle this case.
I can deal with this case.

Interested in Language
Are any differences between two sentences?
I can handle this case.
I can deal with this case.
Not a teacher
To deal with a problem or task is to take action on it, without assurance of success, but to be able to handle something goes one step further - to able to manage it or deal with it successfully to produce results.
I am not a teacher or a native speaker.
Actually, to me they mean the same thing: I can handle it. I can deal with it. I can manage it. I can take care of it. I'm capable of taking responsibility for it. I don't need any help.
I'm not a teacher. I speak American English. I've tutored writing at the University of Southern Maine and have done a good deal of copy editing and writing, occasionally for publication.
I agree with Charlie, and I'd say 'Are there any differences between the two sentences below?'
Typically, you can expert to hear:
I can handle this.
Not a professional teacher