Hi YammiePang,
Would you further share some information on the situation for us to know it better?
1. I notice you posted this thread in Office 365 for Mac forum, so is the Office suite you installed Office for Mac?
2. Would you give us a sketch of the steps of "sign into my Microsoft account" you take before the error pops out? We would like to look into them closely.
3. Please share a screenshot of the error message you got.
To insert a screenshot, please click Use rich formatting > 
Insert/Edit Media.
If the case is you are using Office for Mac 2011, you may refer to Error code 0x80000008 section in I get an error when I try to install Office for Mac 2011, and feel free to share any updates with us.
Please post back at your convenience and we will follow up on your case.
Best Regards,
Rene