There is a tiny doorpost on the inside of the door but there's not enough room for a slanted placement. On the outside the door is flush with the wall so there is no doorpost to place it on at all, even vertically.
Similar to these doors:
It is important to ask these questions to a rabbi, and to send pictures if asking remotely, as small details can have important consequences.
In general, if there is no space on the doorpost, one can drill into it (and I saw new appartments in Israel where every mezuza was drilled into the doorposts - some prefer it this way halachically).
Place the mezuza outside the door but within the door frame. If not possible, you may place the mezuza inside the door frame.
Note: You may recess a mezuza into the door frame.
In extenuating circumstances, such as the aforementioned examples, it would be preferred to drill a hole, less than a handbreadth deep, into the doorpost and place the mezuza into the groove.
If that is not possible, then it would be permitted to affix the mezuza behind the door provided it was placed on the doorpost under the lintel. [see picture on top of p. 4]