How on earth can having no contact with your ex make it possible to get him/her back into your life again? It's simple really, it is said that absence makes the heart grow fonder, and, if you have no contact at all, there is every possibility that your ex will miss having you around, and to win your ex back as well.
Of course you feel that you won't be able to do this right now - you are already missing your ex, and want more than anything in the world to be able to see him/her again.
I understand that you feel like this, but if you want to be able to convince your ex to come back to you, there are certain things that HAVE to be done first, before you can try to win your ex back.
One VERY important thing is to give each other time to get over the troubles of the break up.
You are both terrible hurt and angry with each other right now, so it will be really difficult to have a relaxed conversation and sort out any problems that you both have.
So, give yourself time to feel better naturally - don't try to force convince yourself that you are feeling great, when in reality, you are very depressed.
You need to heal properly inside and your ex as well, and, until this happens, there is no point in getting together just yet.
Slowly but surely, the bad feelings will disappear, and your true feelings for your ex will be strong again - now is the time to think about the problems you both had in your relationship and what you can possibly do to solve them.
Call up your ex and suggest a meeting.
Say that you would like to talk things over, that you both said things that shouldn't have been said, and that you would like a chance to apologize personally.
The chances are that your ex also feels really bad about the stupid argument that you had, and also has some things to say to you as well.
Your ex is missing you a lot now, and is eager to see you again, so there is a very good chance that you will win your ex back.