I'm looking to brush up on my formal knowledge of economic theory and in reading Sanjay Rode's "Advanced Macroeconomics" (ISBN 978-87-403-0156-4) I've come across the following passage (pp 12-13):

In the modern world, all the economies are open economies and we cannot neglect external sector. Foreign trade is a must in the globalized world and it is increasing with increase in openness of a country’s economy. Including these factors, it can be interpreted as follows

Y= C + I + G + (X - M) (1.7) Where (X - M): Net exports to other countries

All governments encourage export and try to minimize imports. The aim is to increase the foreign capital flow and reserves. Including net exports is not enough for equilibrium in the balance of payment. Capital flow is also taken into consideration. It can be interpreted as

Y = C + I + G + (TR-TA) (1.8) Where TR: Total Receipts TA: Total Payments

A total receipt comprises the capital flow and net exports. Similarly, the total payments comprises of the capital outflow and payment for import.

My issue is that, if you combine equations 1.7 and 1.8, you get

X - M = TR - TA (1.9)

Which doesn't seem to make sense, as the entire purpose of introducing the concepts of total receipts and payments was to make a distinction between just net exports and net exports and capital flow. If you try to define total receipts (TR) as, say, net exports plus capital inflow (X - M + CI where CI is capital inflow) as the text implies, and interpret payment for import as the value of imports (M), then you get

X - M = X - M + CI - CO - M CI - CO = M

Where CO is capital outflow. Which would imply that net capital inflow is equal to the value of imports (?). Not sure if I'm missing some nuance or not understanding a definition, or if this just isn't a reputable textbook. The latter seems likely based on the overall quality of the text to be honest.

I think you are overthinking it.

Based on my reading of the text it says that one way of modeling open economy is as:

$$Y_1= C+I+G+(X-M).$$

And alternative to this way is to use model with:

$$Y_2 = C+I +G + (TR-TA).$$

However, the text does not seem to claim that $$Y_1=Y_2$$. Hence you can't just substitute 1.8 into 1.7. The text is saying;

Including net exports is not enough for equilibrium in the balance of payment.

"A total receipt comprises the capital flow and net exports. Similarly, the total payments comprises of the capital outflow and payment for import."

$$TR = X +$$ capital flows

$$TP = M +$$ capital outflows

The open economics modelling $$Y=C+I+G+X-M$$ is a simplification. In reality, you would need to add all the Balance of Payment, i.e current account (roughly X-M), capital account (roughly nothing), and the financial account (capital inflows - capital outflows).

As the Balance of Payment is always equals to 0, current account balance (X-M) is equal to financial account balance. Apparently is the book you mention, the author takes everything into account in $$TR$$ and $$TA$$, i.e the balance of total receipts (from exports and capital inflows) and total payments (imports and capital outflows).