What did you do with the fonts you brought home? Best thing would be to put them in a "Document fonts" (without quotes) folder, and put that in the same folder with the .indd file. ID will then use those fonts (if it can) instead of conflicting fonts already on your system.
Thanks Peter. I just tried that. Still no luck.
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Which version of ID? Which OS on each machine, and the name of the font file, including the extension?
What version of InDesign? What O/S on both machines? You say you're bringing home the files...how? Use file>package and you should get a document fonts folder which will work as long as you're using OpenType fonts.
Sounds like the fonts at work are not.
Indesign CC 2014
Mac OS X
Thanks Bob. I didn't bring the fonts home at first because I had them at
home already. And then when there were problems I asked a colleague to
email me a zip with the fonts. But thanks for the advice, in future will
always package before 'wetranferr'ing.
The fonts folder should be working, so the problem now is probably that you've already changed the fonts.