Albert Barnes' Notes have expounded rather clearly in this case.
I would adjourn this research at the junction of two possibilities:
1. That Matthew gives the account of Joseph's line from David; and Luke gives us Mary's from David.
2. Most acceptable one, that is according to the historian and church father, Africanus, that is as far as Joseph(husband of Mary mother of Jesus)'s father is in concern, there are intermingling of family lines of kinsman or brotherhood according to the law regarding how a brother must take the widow of his deceased brother.
"Matthan, descended from Solomon, married Estha, of whom was born Jacob. After Matthan’s death, Matthat being of the same tribe, but of another family, married his widow, and of this marriage Heli was born. Jacob and Heli were therefore children of the same mother. Heli dying without children, his brother Jacob married his widow, and begat Joseph, who was thus the legal son of Heli. This is agreeable to the account in the two evangelists. Matthew says that Jacob begat Joseph; Luke says that Joseph was the son of Heli, i. e., was his legal heir, or was reckoned in law to be his son."