My idea was that both signals are positive, but for example 5V apart from each other. For example if Tx+_1 is +5V, then Tx+_2 is 0V at that time or if Tx+_1 is +10V, then Tx+_2 is 5V at the same time etc.
And what does the receiver do? Just look at Tx+_2 and ignore Tx+_1 because it's completely redundant information??
Suppose that the transmitter transmits Tx+_1 = +5V, and Tx+_2 = 0V. I suppose this represents the transmitter sending a "0V" signal. Now,
Scenario A: The transmitter decides to send a "5V" signal, so it sends Tx+_1 = +10V, and Tx+_2 = 5V. Fine, the receiver can suppose that a "5V" signal is being sent.
Scenario B: Someone turns on a vacuum cleaner in the vicinity, or something else switches on on the same PCB, inducing a noise current in the two wires carrying Tx+_1 and Tx+_2, causing those wires to briefly increase by 5V. So the receiver sees Tx+_1 = +10V, and Tx+_2 = 5V briefly, which looks exactly like the transmitter is sending a "5V" signal. This is obviously an error. Bad. Etc.
This is the key point: noise induced on twisted pair or side-by-side traces on a PCB is
common mode noise, which means that it appears almost equally on both wires. If you're just sending the same signal on both wires, your signal is common mode as well, which means that the receiver cannot tease apart the signal from the noise. Adding a DC offset to one of the signal achieves nothing useful. If you're sending the signal as a differential signal (Tx+ swings up while Tx- swings down, even though the polarity of both might remain positive at all times), then it's trivial to eliminate the noise and recover the signal: subtract Tx- from Tx+, and almost all the noise will cancel out.
And, as already explained, a differential transmitter sends exactly opposite currents through the two wires, which means that the radiated emissions basically cancel out, which is another nice bonus.