Time for a history lesson!
It turns out that it is difficult to make vacuum tubes and transistors of a precise and stable gain, but quite easy to make them of a "very high gain".
Op-amps created from transistors or vacuum tubes thus share this property. It is difficult to create an op-amp of a precise and stable gain but very easy to make op-amps of a "very high gain".
Story has it that Harold Black was sitting on the train home from work from Bell Labs and it suddenly came to him that negative feedback could be used to obtain mass producible, accurate and stable gains in spite of this problem.
Negative feedback lets you take advantage of a "very high" but not very precise gain and puts all the gain accuracy and stability onto the external components used. It is much easier to make precise and stable resistors. Not to mention it is much cheaper to make a wide range of resistor values than it is to make an semiconductor amplifier and every possible gain that might be needed.
So in theory you could use make an amplifier out of transistors for a particular gain without resistors. But it will be difficult to make and that gain will not be very stable over over a wide range of input voltages, temperatures, or supply voltages.
You cannot do this with an op-amp since op-amp are specifically designed to offload all the gain accuracy and stability from the transistors inside the opamp to the resistors (and other passive components) on the outside.
So to make a subtract voltages, use opamps and resistors. This is what they were made for.
You may need to do jump through some hoops doing things that seem ackward and strange compared to the neat and tidy math on paper.
For example, summing involves running each input voltage through a resistor to a shared node. And the relative resistances used contribute a weight to each input voltage, so there are always weights. There is no such thing as unweighted but you can have equal weighting.
But these also form a voltage divider of sorts so the final result is also smaller than what you know it should be at which point you must use an opamp+resistors to re-amplify it to offset this (or larger or smaller, whatever you want really).
You're getting into things that are best off understood using KVL circuit analysis which if you don't know, can learn, or you can just find canned circuits with equations online such as this:
If you want a negative input you going to need negative voltages. If you have a positive input you want to convert to a negative input, you can do this by multiplying by -1 which is what an inverting amp with a gain of 1 will do.
However, note that opamps can only accept voltage inputs and produce output voltages within their voltage supply range. Often they can't even do this as most op-amps will not have their input and output range cover the entire supply range. It often falls short by about 3V on either side. Thee so-called "common-mode input range" and "output range" on the datasheet. That means that if you want to use something like -2V as an input or have -2V as an output then you will need an to provide a supply voltage that includes -2V (plus aforementioned overhead) in its range.