After confirming you have an enterprise developer account and the account is actually under the company, I'm assuming this app is solely an internal-app for the company the developer account is under. This means you can leverage OTA or Over-The-Air transmission. The first thing you'll need to do is archive the app. In one of the last steps instead of the submission to apple store option, you can select to deliver wirelessly. This will create a plist and an ipa. Note that you need to get all the URLS correct in the plist, including the icon URLs otherwise OTA installation can fail.
So you now have your plist and an ipa. What you need to do is get access to their server. They probably have some server guys already, so all you need to do is hand them a file, or ask for FTP permissions. Now you have two options:
1) Recommend that this app is only on an internal server available only on the company wi-fi. This will make it much more secure so that people don't have access to the app by stumbling across it on the web.
2) Put it on the web behind some authentication and hope the server isn't found/hacked.
Once this has been settled, you now need to point to the plist. What happens is your phone will mimic the iTunes store installation with your plist. You need to point to it via something like:
<a href="itms-services://?action=download-manifest&url=localFilePath/APP.plist">App Link </a>
Note that the href has a special link and keyword. This will tell the iphone that there is an App it should install, using the provided plist URL. The phone will go out and download the pList, which will have the URL for your ipa. The phone will then go out to grab the IPA and start installing.