If you immerse yourself in the problem, it will be solved easily, like oil calming rough waters.
Literal
Problem [to-に] immerse-oneself [if-すれば], oil [subj-が] wind-waves [obj-を] calms [like-ように], easily, that problem [subj-が] dissolves.
没頭する ('immerse oneself, be absorbed') is Sino-Japanese. The simile 油が風波をしずめるように alludes to the notion of 'oil on troubled waters.' ~ば is the conditional. とける ('dissolve, be solved') extends a physical metaphor to problem-solving.