For answering a phone call, this is available only from Android O. Before, it might not work. Here's a code for it:
/**returns true iff we are sure that answering the phone call worked*/
fun answerCall(context: Context): Boolean {
    if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.O) {
        val telecomManager = context.getSystemService(Context.TELECOM_SERVICE) as TelecomManager
        if (ContextCompat.checkSelfPermission(context, Manifest.permission.ANSWER_PHONE_CALLS) == PackageManager.PERMISSION_GRANTED
                || ContextCompat.checkSelfPermission(context, Manifest.permission.MODIFY_PHONE_STATE) == PackageManager.PERMISSION_GRANTED) {
            telecomManager.acceptRingingCall()
            return true
        }
        return false
    }
    // https://stackoverflow.com/a/29651130/878126
    // for HTC devices we need to broadcast a connected headset
    val audioManager = context.getSystemService(Context.AUDIO_SERVICE) as AudioManager
    val broadcastConnected = "htc" == Build.MANUFACTURER.toLowerCase(Locale.US) && !audioManager.isWiredHeadsetOn
    if (broadcastConnected)
        broadcastHeadsetConnected(context, false)
    try {
        try {
            Runtime.getRuntime().exec("input keyevent " + Integer.toString(KeyEvent.KEYCODE_HEADSETHOOK))
        } catch (e: IOException) {
            // Runtime.exec(String) had an I/O problem, try to fall back
            val enforcedPerm = "android.permission.CALL_PRIVILEGED"
            val btnDown = Intent(Intent.ACTION_MEDIA_BUTTON).putExtra(Intent.EXTRA_KEY_EVENT, KeyEvent(KeyEvent.ACTION_DOWN, KeyEvent.KEYCODE_HEADSETHOOK))
            val btnUp = Intent(Intent.ACTION_MEDIA_BUTTON).putExtra(Intent.EXTRA_KEY_EVENT, KeyEvent(KeyEvent.ACTION_UP, KeyEvent.KEYCODE_HEADSETHOOK))
            context.sendOrderedBroadcast(btnDown, enforcedPerm)
            context.sendOrderedBroadcast(btnUp, enforcedPerm)
        }
    } finally {
        if (broadcastConnected)
            broadcastHeadsetConnected(context, false)
    }
    return false
}
For hanging up a call, this was added officially on Android P, but the workaround seems to work on most cases I've tried so far (doesn't work on Nexus 5x with Android 8.1, for example) . Here's code for this :
@SuppressLint("PrivateApi")
fun endCall(context: Context): Boolean {
    if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.P) {
        val telecomManager = context.getSystemService(Context.TELECOM_SERVICE) as TelecomManager
        if (telecomManager != null && ContextCompat.checkSelfPermission(context, Manifest.permission.ANSWER_PHONE_CALLS) == PackageManager.PERMISSION_GRANTED) {
            telecomManager.endCall()
            return true
        }
        return false
    }
    //use unofficial API for older Android versions, as written here: https://stackoverflow.com/a/8380418/878126
    try {
        val telephonyClass = Class.forName("com.android.internal.telephony.ITelephony")
        val telephonyStubClass = telephonyClass.classes[0]
        val serviceManagerClass = Class.forName("android.os.ServiceManager")
        val serviceManagerNativeClass = Class.forName("android.os.ServiceManagerNative")
        val getService = serviceManagerClass.getMethod("getService", String::class.java)
        val tempInterfaceMethod = serviceManagerNativeClass.getMethod("asInterface", IBinder::class.java)
        val tmpBinder = Binder()
        tmpBinder.attachInterface(null, "fake")
        val serviceManagerObject = tempInterfaceMethod.invoke(null, tmpBinder)
        val retbinder = getService.invoke(serviceManagerObject, "phone") as IBinder
        val serviceMethod = telephonyStubClass.getMethod("asInterface", IBinder::class.java)
        val telephonyObject = serviceMethod.invoke(null, retbinder)
        val telephonyEndCall = telephonyClass.getMethod("endCall")
        telephonyEndCall.invoke(telephonyObject)
        return false
    } catch (e: Exception) {
        e.printStackTrace()
        return false
    }
}
So, for both answering and rejecting calls, the safest way to do it, is to have it run on Android P... :(