I took an empty sheet of paper, wrote your statements on each side, and the earth didn't stand still, no angry god come down to earth and destroyed the paper, nothing happened. So it's not a bad deal.
I can make four different statement now of the form "the statement on the front of the paper is true/false, and the statement on the back is true/false". Of these four different statements, two are consistent with what is written on the paper: "the statement on the front of the paper is true, and the statement on the back is false" and "the statement on the front of the paper is false, and the statement on the back is true".
Mockingbird: I don't get what you don't get.
First, you call it a paradox, I call it two sentences written on a sheet of paper. That means there is no big problem to solve here. It's nothing to worry about.
Second, there are two statements, each could be true or false, making four combinations. Two of these four combinations are consistent with what is written. This is different from the standard liar paradox, where "the liar's statement is true" and "the liar's statement is false" are both inconsistent with the liar's statement.
So we don't actually have a paradox at all - we know definitely that one statement is true and one is false, we just cannot say which one.