2 PWM signals out of phase

Create one, and use a transistor to invert it.
Otherwise, use blink-without-delay and flip two outputs at every time change:

unsigned long currentTime;
unsigned long previousTime;
unsigned long elapsedTime;
unsigned long duration = 50; //  toggle output every 50uS, 10KHz output
byte pin2 = 2; // PORTD bit2
byte pins = 3; // PORTD bit3
void setup(){
pinMode (pin2, OUTPUT);
digitalWrite (pin2, HIGH);
pinMode (pin3, OUTPUT);
digitalWrite (pin3, LOW);
}
void loop(){
currentTime = micros();
elapsedTime = currentTime - previousTime;
if (elapsedTime >=duration){
  previousTime = previousTime + duration;
  PIND = PIND | 0b00001100; // toggle outputs by writing 1 to input port
  }
// do other stuff while waiting for duration to pass. Must finish in < duration uS, or software PWM will be affected
}