My husband of 18 years walked out on myself and ...

Hi,
Yes there is a chance, But:
1.  You are not on any kind
     of "test".
2.  He knows you and he
     accepts you as you are. 
3.  He really and honestly
     promises to do all he can
     to bring your relations
     back to track. 
4.  You believe him and
     believe he is able.
5.  You are able to both
     forgive him and forget it.
6.  You promise never to
     mention it.
I wish you the best of luck and hope you'll succeed.
Best regards,

there is always a chance. the real question is do you both love each enough to overcome the problem. it will take both of you working together to save your marriage, even though you did not cause the initial problem. the best to you both, i really hope you do save your marriage in a world where most people consider marriage disposable.

Hi,

   Both OronD and woosmajogin gave you excellent answers.  I gave them 2 thumbs up each.

   It's good that both of you decided to get back together.  The only thing is you need to see if you'll be able to forgive and also forget his offense.  If you take him back, don't mention it again to him.  It will just create animosity.  The children will be very pleased that you are getting back together.  You are aware that it will take a lot of work for you both to get back the normal life  that you had  before he left you.  Try hard to be a loving and caring wife inspite of everything.

Hope you'll have a happier life together this time.

This is a hard one , you have received some excellent advice .   And I am glad you and your husband are working on saving your marriage .   I have one question and it is the first thing that popped in my head while reading your question .  He says he loves you but is in love with the other woman .    Here's my question .....  Are you sure your husband ended the affair or did she end it and he's come home with his tail tucked between his legs , because he's got no other place to go .  I am sorry to ask this but if I were in your shoes I would want to know in my heart that he is sincere in wanting to save your marriage , before I started giving my heart back to him .  Think this is a important question that you need an answer to . 

There is a reason your husband left you for another woman.  Both of you need to be totally honest if you are going to try to fix the mess you are in.  If he found something in the other woman that you cannot give, then it is not going to work.  If he got bored, then that is something you two can work on together.  It is very hard to forget that someone hurts you that badly.  But, forgiveness goes a very long way towards mending a broken marriage.  He needs to look at himself closely and tell you honestly why he left, and if he doesn't know, he needs to see a professional.  You cannot work on a problem if you don't know or understand its cause.  And him just moving back in and you two pretending nothing happened but trying to spark things up won't work.  It would be like putting a Band-aid on a cut that requires a tourniquet.  Talk, search, explore, and by all means, do not change to please him.  Be yourself.  If you are meant to be together it has to be the real you, and not some fantasy wife he wants.