Will the N- or the C- terminal soluble domain be on the extracellular side?
Luminal/cytoplasmic orientation of single-pass transmembrane proteins is mostly dictated by positively charged residues residing on the cytoplasmic side (positive-inside rule) and negatively charged residues being suppressed on the cytoplasmic side/preferred on the luminal side (negative inside depletion/outside enrichment rule).

Since your molecule has a positively charged Lys residue on its N-terminus and a negative negatively charged Glu residue on its C-terminal side your protein would most likely acquire a type II integral membrane protein topology, i.e. the C-terminal part would be directed towards the extracellular space while the N-terminal part is in the cytosol.

Further references can be found here:

Baker JA et al., Charged residues next to transmembrane regions revisited: “Positive-inside rule” is complemented by the “negative inside depletion/outside enrichment rule” BMC Biol. 2017 pubmed  

Ott CM and Lingappa VR, Integral membrane protein biosynthesis: why topology is hard to predict. J. Cell. Sci. 2002 pubmed