Quick, does this sentence make sense?
 

Eager to share with you how my excellent problem-solving skills and leadership potential can benefit SHCC, I look forward to speaking with you soon.

Re: Quick, does this sentence make sense?
 

It would be better to reverse the fragments. The first fragment is much too long so it sounds a little funny. This is how I would write it.

Re: Quick, does this sentence make sense?
 

Good call

Re: Quick, does this sentence make sense?
 

I hate drama.

Re: Quick, does this sentence make sense?
 

I yearn with excitement at the prospect of speaking with you, as doing so will allow me the privilege to prove worthy my ability to problem solve and demonstrate admirable leadership skills.