Objection 1. It would seem that sadness does not cause pleasure. For nothing causes its own contrary. But sadness is contrary to pleasure. Therefore it does not cause it.
Objection 2. Further, contraries have contrary effects. But pleasures, when called to mind, cause pleasure. Therefore sad things, when remembered, cause sorrow and not pleasure.
Objection 3. Further, as sadness is to pleasure, so is hatred to love. But hatred does not cause love, but rather the other way about, as stated above (Question 29, Article 2). Therefore sadness does not cause pleasure.
On the contrary, It is written (Psalm 41:4): "My tears have been my bread day and night": where bread denotes the refreshment of pleasure. Therefore tears, which arise from sadness, can give pleasure.
I answer that, Sadness may be considered in two ways: as existing actually, and as existing in the memory: and in both ways sadness can cause pleasure. Because sadness, as actually existing, causes pleasure, inasmuch as it brings to mind that which is loved, the absence of which causes sadness; and yet the mere thought of it gives pleasure. The recollection of sadness becomes a cause of pleasure, on account of the deliverance which ensued: because absence of evil is looked upon as something good; wherefore so far as a man thinks that he has been delivered from that which caused him sorrow and pain, so much reason has he to rejoice. Hence Augustine says in De Civ. Dei xxii, 31 [Gregory, Moral. iv.] that "oftentimes in joy we call to mind sad things... and in the season of health we recall past pains without feeling pain... and in proportion are the more filled with joy and gladness": and again (Confess. viii, 3) he says that "the more peril there was in the battle, so much the more joy will there be in the triumph."
Reply to Objection 1. Sometimes accidentally a thing is the cause of its contrary: thus "that which is cold sometimes causes heat," as stated in Phys. viii, 1. In like manner sadness is the accidental cause of pleasure, in so far as it gives rise to the apprehension of something pleasant.
Reply to Objection 2. Sad things, called to mind, cause pleasure, not in so far as they are sad and contrary to pleasant things; but in so far as man is delivered from them. In like manner the recollection of pleasant things, by reason of these being lost, may cause sadness.
Reply to Objection 3. Hatred also can be the accidental cause of love: i.e. so far as some love one another, inasmuch as they agree in hating one and the same thing.
Source: Summa Theologica (New Advent)