In this case, only the total capital stock k is predetermined. Hence, you have to use a law of motion for capital
k = (1-delta)*k(-1) + iThe total capital stock in the economy k(-1), which was decided by investment in the period before (hence the (-1) timing), can be freely divided between the individual sectors. Hence, kT and kN are determined at time t and not predetermined (normal variables). The corresponding resource constraint thus reads
k(-1) = kT + kN