If you're sending binary data over a serial line, you really shouldn't confuse everything by using a text-style linefeed separator.
On the other hand, it's kind of hard (for the other end) to know which byte is which, without some kind of synchronization help.
But, since you only have 10 bits of payload, but send 16 bits of data, you can "do a UTF-8" and use a free bit to signal "start of value". This will require using only 7 bits of each 8-bit byte for your payload, but that's fine since 7 + 7 = 14 which is way more than 10. We can let the 8th bit mean "this is the high byte of a new pair of bytes":
const int a = 600;
const unsigned char high = ((a >> 7) & 0x7f) | 0x80;
const unsigned char low = (a & 0x7f);
Serial.print(high);
Serial.print(low);
In the above, the two bytes transmitted will be:
high == ((600 >> 7) & 0x7f) | 0x80 == 4 | 0x80 == 0x84
low == (600 & 0x7f) == 88 == 0x58
The receiver will have to do the above in reverse:
const int value = ((high & 0x7f) << 7) | low;
This should work, and uses the most-significant bit of the high byte, which is sent first, to signify that that is indeed the high byte. The low byte will never have the MSB set.