195964

Since 0+0=0, nothing can be zero, as every number doesn't link to itself. 1234/2 = 617, so TWO>617. Since 2T = FO, F, and therefore O is even. Let's say it's 8. Since 18/2 = 9, T=9, F=1, and O=8. Two eights are 16, carry the one, so R=6. You can test different values of W, but let's say it's 2. 2+2+1(carried)=3: U=3. This is just one solution: O can be any even number except 0. But 928 + 928= 1856 is still one.
As for the second part, you can use similar logic, but for ONE + TWO = THREE, two 3-digit numbers add to a 4-digit at maximum. ONE + THREE = FOUR is also impossible: a 5-digit > 4-digit, and there's no such thing as negative digits.