I know about using den/dan sonra

but what about expressing the time

for example

10 gün sonra

or

10 günden sonra

teşekkür ederim

"10 gün sonra" is the correct form.You have to not use "den" to add "gün".. 

Time expressions are so often simplified forms of the corresponding grammatical structures. I usually just guess them and make them look as simle as possible. But if one of the natives cleared these issues (dropped case endings in time expressions) it would be so good.

x-den sonra = after x

x-den önce = before x

x is a reference point here

sometimes there may be a displacement included:

x-den y dakika/saat/gün/hafta/ay/yıl/etc. önce/sonra (time)

= y minutes/hours/days/weeks/months/years/etc. earlier/later than x

with "x-den" part missing/dropped above (in a clear context)

y dakika/saat/gün/hafta/ay/yıl/etc. önce/sonra

= y minutes/hours/days/weeks/months/years/etc. ago/later

x-den y adım/metre/km/cm/etc. önce/sonra (space)

= y steps/meters/kms/cms/etc. before/after

x dakika/saat/gün/hafta/ay/yıl/etc -den sonra = after (passing/having passed) x minutes/hours/days/weeks/months/years/etc.

x adım/metre/km/cm/etc. -den sonra = after (going/having gone) x steps/meters/kms/cms/etc.

x dakika/saat/gün/hafta/ay/yıl/etc -den önce = before (passing/having passed) x minutes/hours/days/weeks/months/years/etc.

x adım/metre/km/cm/etc. -den önce = before (going/having gone) x steps/meters/kms/cms/etc.

Examples:

2 saatten sonra gitti = he/she left after spending 2 hours (here)

2 saatten önce gitme = don´t leave (here) before having passed 2 hours

2 km.den sonra durup dinlendik = after going 2 kms we stopped and rested

100 metreden önce durma = don´t stop before going 100 meters.

etc.

"Displacement". Yes.

The structure is so much simplified you should expect ambiguity but obviously there is none.

si++, sağ ol. We will probably refer to your post many times later.