Have equity in home count as part of down payment?

[Jessica Tucker Grubbs]

Appraisal= $258k/ purchase price = $230k/ Built-in Equity= $28,000/ Down payment cash $27,000.

I have $27,000 cash to put into a down payment on the above home BUT, I need to use some (about $10,000) for a new roof/gutters.  Is there a way I can get a mortgage that will not have PMI due to the level of equity in the home and I can put down only $17-18k instead of the full $27k? Or do you have any other advice on how to pull this off? (Not interested in 203k loan due to difficulty level/finding broker to help).

If it is worth anything the home may appraise for slightly more now as it has a brand new furnace/HVAC and white 6ft perimeter vinyl fence since the last appraisal in April 2019. 

I will also be in need of a rapid rescore after paying off large credit card balances.

Any NC mortgage folks that know how to pull this off?