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Before moving on, I would like to confirm if you are using Office 365 Enterprise version or Office 365 Small business version.
For Office 365 E plan, you would just download Office Professional Plus in Office 365 Portal by following the steps below:
1. Log into Office 365 Portal (MOP) and click Admin from the top header.
2. Click Downloads from the Admin page.
3. At the download page, click Install under the first option to install Microsoft Office Professional Plus.
For Office 365 P plan, you would need to purchase Office Professional Plus additionally to get Outlook 2010.
Here are two links for your reference:
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