We will need a lot of information to help with this issue. First, what method are you using to install Office? Are you using a script, or launching setup.exe with command line parameters and a config file generated via the deployment tool for Office? Whatever method you are using, it's vital to test it manually first and ensure it's successful before expecting it to work via LANDesk. Be sure to use the same process manually that you are using via landesk.
There are many options to installing MS Office but one method I've had great luck with is documented here: Best Known Methods for Installing Office 365 Click-to-Run
While that doc mentions 2016 and 2013 versions, there is a 2010 version of the deployment tool available that should work for you.
I already have found the problem and the solution.
It is very important to uninstall all previous OFFICE versions.
I used a special tool from MICROSOFT to do this, called : O15-ctrRemove.diagcab
Later on it was possible to distribute just my OFFICE2010 or OFFICE2013.
And the DEPLOY provisioning template was also successful.
That's great I am glad to hear it. I'm glad that process is working for you. For your information if you use the office customization tool there is an option to automatically uninstall other versions of MS Office. If your current process is working then there is probably no need, but it's usually a more streamlined process with less steps.