What I can do to get a divorce when my husband has been out of the country for 10 years and I have no contact with him?

There is something known as "divorce by publication" which is used for the very circumstance that you have here - a spouse whose whereabouts are unknown. By way of background, in any legal proceeding the concept of "notice" is critical. Legal action cannot be taken against someone without giving them the right to appear and explain their side of things. Therefore, even if a spouse can't be located they still must be notified of the divorce action before it can proceed. 

Divorce by publication typically works like this - you as the filing spouse (i.e. petitioner) must make a good faith effort to find your missing spouse (i.e. respondent).  You will have to present proof to the court that you made a true effort to locate him; for example by searching near his last known address. Once you have demonstrated to the the court's satisfaction that you have made a diligent search, you will be allowed to serve your spouse by publishing notice in a newspaper as opposed to personally serving them (the court will instruct as to which paper should be used).  

Generally, the respondent has 30-60 days to file a reply. If they fail to respond within that time the petitioner files a request to enter a "divorce by default" (although the respondent is given a certain time limit in which they can appeal).

In your case, since your husband is living out of the country, the notice requirements will be somewhat more complicated.  So you best bet is to hire an attorney that has experience in this type of divorce. You want to make sure that you follow all required steps; this isn't something that you want to get wrong.